# RD Sharma solutions for Class 11 Mathematics Textbook chapter 22 - Brief review of cartesian system of rectangular co-ordinates [Latest edition]

#### Chapters ## Chapter 22: Brief review of cartesian system of rectangular co-ordinates

22.122.222.3Others

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 22 Brief review of cartesian system of rectangular co-ordinates 22.1 [Pages 12 - 13]

22.1 | Q 1 | Page 12

If the line segment joining the points P (x1, y1) and Q (x2, y2) subtends an angle α at the origin O, prove that
OP · OQ cos α = x1 x2 + y1, y2

22.1 | Q 2 | Page 13

The vertices of a triangle ABC are A (0, 0), B (2, −1) and C (9, 2). Find cos B.

22.1 | Q 3 | Page 13

Four points A (6, 3), B (−3, 5), C (4, −2) and D (x, 3x) are given in such a way that $\frac{\Delta DBC}{\Delta ABC} = \frac{1}{2}$. Find x.

22.1 | Q 4 | Page 13

The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.

22.1 | Q 5 | Page 13

Find the coordinates of the centre of the circle inscribed in a triangle whose vertices are (−36, 7), (20, 7) and (0, −8).

22.1 | Q 6 | Page 13

The base of an equilateral triangle with side 2a lies along the y-axis, such that the mid-point of the base is at the origin. Find the vertices of the triangle.

22.1 | Q 7 | Page 13

Find the distance between P (x1, y1) and Q (x2, y2) when (i) PQ is parallel to the y-axis (ii) PQ is parallel to the x-axis.

22.1 | Q 8 | Page 13

Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 22 Brief review of cartesian system of rectangular co-ordinates 22.2 [Page 18]

22.2 | Q 1 | Page 18

Find the locus of a point equidistant from the point (2, 4) and the y-axis.

22.2 | Q 2 | Page 18

Find the equation of the locus of a point which moves such that the ratio of its distances from (2, 0) and (1, 3) is 5 : 4.

22.2 | Q 3 | Page 18

A point moves so that the difference of its distances from (ae, 0) and (−ae, 0) is 2a. Prove that the equation to its locus is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$

22.2 | Q 4 | Page 18

Find the locus of a point such that the sum of its distances from (0, 2) and (0, −2) is 6.

22.2 | Q 5 | Page 18

Find the locus of a point which is equidistant from (1, 3) and the x-axis.

22.2 | Q 6 | Page 18

Find the locus of a point which moves such that its distance from the origin is three times its distance from the x-axis.

22.2 | Q 7 | Page 18

A (5, 3), B (3, −2) are two fixed points; find the equation to the locus of a point P which moves so that the area of the triangle PAB is 9 units.

22.2 | Q 8 | Page 18

Find the locus of a point such that the line segments with end points (2, 0) and (−2, 0) subtend a right angle at that point.

22.2 | Q 9 | Page 18

If A (−1, 1) and B (2, 3) are two fixed points, find the locus of a point P, so that the area of ∆PAB = 8 sq. units.

22.2 | Q 10 | Page 18

A rod of length l slides between two perpendicular lines. Find the locus of the point on the rod which divides it in the ratio 1 : 2.

22.2 | Q 11 | Page 18

Find the locus of the mid-point of the portion of the line x cos α + y sin α = p which is intercepted between the axes.

22.2 | Q 12 | Page 18

If O is the origin and Q is a variable point on y2 = x, find the locus of the mid-point of OQ.

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 22 Brief review of cartesian system of rectangular co-ordinates 22.3 [Page 21]

22.3 | Q 1 | Page 21

What does the equation (x − a)2 + (y − b)2 = r2 become when the axes are transferred to parallel axes through the point (a − c, b)?

22.3 | Q 2 | Page 21

What does the equation (a − b) (x2 + y2) −2abx = 0 become if the origin is shifted to the point $\left( \frac{ab}{a - b}, 0 \right)$ without rotation?

22.3 | Q 3.1 | Page 21

Find what the following equation become when the origin is shifted to the point (1, 1).
x2 + xy − 3x − y + 2 = 0

22.3 | Q 3.2 | Page 21

Find what the following equation become when the origin is shifted to the point (1, 1).
x2 − y2 − 2x +2y = 0

22.3 | Q 3.3 | Page 21

Find what the following equation become when the origin is shifted to the point (1, 1).
xy − x − y + 1 = 0

22.3 | Q 3.4 | Page 21

Find what the following equation become when the origin is shifted to the point (1, 1).
xy − y2 − x + y = 0

22.3 | Q 4 | Page 21

To what point should the origin be shifted so that the equation x2 + xy − 3x − y + 2 = 0 does not contain any first degree term and constant term?

22.3 | Q 5 | Page 21

Verify that the area of the triangle with vertices (2, 3), (5, 7) and (− 3 − 1) remains invariant under the translation of axes when the origin is shifted to the point (−1, 3).

22.3 | Q 6.1 | Page 21

Find what the following equation become when the origin is shifted to the point (1, 1).
x2 + xy − 3y2 − y + 2 = 0

22.3 | Q 6.2 | Page 21

Find what the following equation become when the origin is shifted to the point (1, 1).
xy − y2 − x + y = 0

22.3 | Q 6.3 | Page 21

Find what the following equation become when the origin is shifted to the point (1, 1).
xy − x − y + 1 = 0

22.3 | Q 6.4 | Page 21

Find what the following equation become when the origin is shifted to the point (1, 1).
x2 − y2 − 2x + 2y = 0

22.3 | Q 7.1 | Page 21

Find the point to which the origin should be shifted after a translation of axes so that the following equation will have no first degree terms:  y2 + x2 − 4x − 8y + 3 = 0

22.3 | Q 7.2 | Page 21

Find the point to which the origin should be shifted after a translation of axes so that the following equation will have no first degree terms: x2 + y2 − 5x + 2y − 5 = 0

22.3 | Q 7.3 | Page 21

Find the point to which the origin should be shifted after a translation of axes so that the following equation will have no first degree terms: x2 − 12x + 4 = 0

22.3 | Q 8 | Page 21

Verify that the area of the triangle with vertices (4, 6), (7, 10) and (1, −2) remains invariant under the translation of axes when the origin is shifted to the point (−2, 1).

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 22 Brief review of cartesian system of rectangular co-ordinates [Pages 21 - 22]

Q 1 | Page 21

The vertices of a triangle are O (0, 0), A (a, 0) and B (0, b). Write the coordinates of its circumcentre.

Q 2 | Page 21

In Q.No. 1, write the distance between the circumcentre and orthocentre of ∆OAB.

Q 3 | Page 21

Write the coordinates of the orthocentre of the triangle formed by points (8, 0), (4, 6) and (0, 0).

Q 4 | Page 21

Three vertices of a parallelogram, taken in order, are (−1, −6), (2, −5) and (7, 2). Write the coordinates of its fourth vertex.

Q 5 | Page 22

If the points (a, 0), (at12, 2at1) and (at22, 2at2) are collinear, write the value of t1 t2.

Q 6 | Page 22

If the coordinates of the sides AB and AC of  ∆ABC are (3, 5) and (−3, −3), respectively, then write the length of side BC.

Q 7 | Page 22

Write the coordinates of the circumcentre of a triangle whose centroid and orthocentre are at (3, 3) and (−3, 5), respectively.

Q 8 | Page 22

Write the coordinates of the in-centre of the triangle with vertices at (0, 0), (5, 0) and (0, 12).

Q 9 | Page 22

If the points (1, −1), (2, −1) and (4, −3) are the mid-points of the sides of a triangle, then write the coordinates of its centroid.

Q 10 | Page 22

Write the area of the triangle with vertices at (a, b + c), (b, c + a) and (c, a + b).

## Chapter 22: Brief review of cartesian system of rectangular co-ordinates

22.122.222.3Others ## RD Sharma solutions for Class 11 Mathematics Textbook chapter 22 - Brief review of cartesian system of rectangular co-ordinates

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Concepts covered in Class 11 Mathematics Textbook chapter 22 Brief review of cartesian system of rectangular co-ordinates are Cartesian Product of Sets, Brief Review of Cartesian System of Rectanglar Co-ordinates, Relation, Functions, Some Functions and Their Graphs, Algebra of Real Functions, Ordered Pairs, Equality of Ordered Pairs, Pictorial Diagrams, Graph of Function, Pictorial Representation of a Function, Exponential Function, Logarithmic Functions.

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