#### 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.