#### Chapters

Chapter 2 - Relations and Functions

Chapter 3 - Trigonometric Functions

Chapter 4 - Principle of Mathematical Induction

Chapter 5 - Complex Numbers and Quadratic Equations

Chapter 6 - Linear Inequalities

Chapter 7 - Permutations and Combinations

Chapter 8 - Binomial Theorem

Chapter 9 - Sequences and Series

Chapter 10 - Straight Lines

Chapter 11 - Conic Sections

Chapter 12 - Introduction to Three Dimensional Geometry

Chapter 13 - Limits and Derivatives

Chapter 14 - Mathematical Reasoning

Chapter 15 - Statistics

Chapter 16 - Probability

## Chapter 11 - Conic Sections

#### Page 241

Find the equation of the circle with centre (0, 2) and radius 2

Find the equation of the circle with centre (–2, 3) and radius 4

Find the equation of the circle with `(1/2, 1/4)`and radius `1/12`

Find the equation of the circle with centre (1, 1) and radius `sqrt2`

Find the equation of the circle with centre (–*a*, –*b*) and radius `sqrt(a^2-b^2)`

Find the centre and radius of the circle (*x* + 5)^{2} + (*y* – 3)^{2} = 36

Find the centre and radius of the circle *x*^{2} + *y*^{2} – 4*x* – 8*y* – 45 = 0

Find the centre and radius of the circle *x*^{2} + *y*^{2} – 8*x* + 10*y* – 12 = 0

Find the centre and radius of the circle 2*x*^{2} + 2*y*^{2} – *x* = 0

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4*x* + *y* = 16.

Find the equation of the circle passing through the points (2, 3) and (–1, 1) and whose centre is on the line *x *– 3*y* – 11 = 0.

Find the equation of the circle with radius 5 whose centre lies on *x*-axis and passes through the point (2, 3).

Find the equation of the circle passing through (0, 0) and making intercepts *a *and *b* on the coordinate axes.

Find the equation of a circle with centre (2, 2) and passes through the point (4, 5).

Does the point (–2.5, 3.5) lie inside, outside or on the circle *x*^{2} + *y*^{2} = 25?

#### Pages 246 - 247

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for *y*^{2} = 12*x*

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for *x*^{2} = 6*y*

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for *y*^{2} = – 8*x*

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for *x*^{2} = – 16*y*

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for *y*^{2} = 10*x*

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for *x*^{2} = –9*y*

Find the equation of the parabola that satisfies the following conditions: Focus (6, 0); directrix *x* = –6

Find the equation of the parabola that satisfies the following conditions: Focus (0, –3); directrix *y* = 3

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0); focus (3, 0)

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) focus (–2, 0)

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along *x*-axis

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0), passing through (5, 2) and symmetric with respect to *y*-axis

#### Page 255

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse `x^2/36 + y^2/16 = 1`

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse `x^2/4 + y^2/25 = 1`

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse `x^2/16 + y^2/9 = 1`

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse `x^2/25 + y^2/100 = 1`

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse `x^2/49 + y^2/36 = 1`

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse `x^2/100 + y^2/400 = 1`

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 36*x*^{2} + 4*y*^{2} = 144

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 16*x*^{2} + *y*^{2} = 16

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 4*x*^{2} + 9*y*^{2} = 36

Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0)

Find the equation for the ellipse that satisfies the given conditions: Vertices (0, ±13), foci (0, ±5)

Find the equation for the ellipse that satisfies the given conditions: Vertices (±6, 0), foci (±4, 0)

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (±3, 0), ends of minor axis (0, ±2)

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (0, `+- sqrt5`), ends of minor axis (±1, 0)

Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (±5, 0)

Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6)

Find the equation for the ellipse that satisfies the given conditions: Foci (±3, 0), *a* = 4

Find the equation for the ellipse that satisfies the given conditions: *b* = 3, *c* = 4, centre at the origin; foci on the *x *axis.

Find the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), major axis on the *y*-axis and passes through the points (3, 2) and (1, 6)

Find the equation for the ellipse that satisfies the given conditions: Major axis on the *x*-axis and passes through the points (4, 3) and (6, 2).

#### Page 262

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola `x^2/16 - y^2/9 = 1`

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola `y^2/9 - x^2/27 = 1`

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 9*y*^{2} – 4*x*^{2} = 36

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16*x*^{2} – 9*y*^{2} = 576

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 5*y*^{2} – 9*x*^{2} = 36

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 49*y*^{2} – 16*x*^{2} = 784

Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8)

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5)

Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.

Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24.

Find the equation of the hyperbola satisfying the give conditions: Foci `(+-3sqrt5, 0)`, the latus rectum is of length 8

Find the equation of the hyperbola satisfying the give conditions: Foci (±4, 0), the latus rectum is of length 12

Find the equation of the hyperbola satisfying the give conditions: Vertices (±7, 0), e = 4/3

Find the equation of the hyperbola satisfying the give conditions: Foci `(0, +- sqrt10)`, passing through (2, 3)

#### Page 264

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the *x*-axis.

Find the area of the triangle formed by the lines joining the vertex of the parabola *x*^{2} = 12*y* to the ends of its latus rectum.

A man running a racecourse notes that the sum of the distances from the two flag posts form him is always 10 m and the distance between the flag posts is 8 m. find the equation of the posts traced by the man.

An equilateral triangle is inscribed in the parabola *y*^{2} = 4 *ax*, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

#### Textbook solutions for Class 11

## NCERT solutions for Class 11 Mathematics chapter 11 - Conic Sections

NCERT solutions for Class 11 Mathematics chapter 11 (Conic Sections) include all questions with solution and detail explanation from Mathematics Textbook for Class 11. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has created the CBSE Mathematics Textbook for Class 11 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11 Mathematics chapter 11 Conic Sections are Sections of a Cone, Standard Equation of a Circle, Standard Equations of Parabola, Latus Rectum, Standard Equations of an Ellipse, Latus Rectum, Standard Equation of Hyperbola, Concept of Circle, Introduction of Parabola, Introduction of Ellipse, Relationship Between Semi-major Axis, Semi-minor Axis and the Distance of the Focus from the Centre of the Ellipse, Special Cases of an Ellipse, Eccentricity, Introduction of Hyperbola, Eccentricity, Latus Rectum.

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