KC Sinha Mathematics Solution Class 11 Chapter 22 Conic Section: Circle Exercise 22.3

 Exercise 22.3

Page no 22.36

Type 1

Question 1

Find the equation of the circle when the end points of a diameter of the circle are :

(i) $(3,4)$ and $(-3,-4)$

(ii) $(-2,3)$ and $(3,-5)$

(iii) $(0,0)$ and $(2,-4)$

(iv) $(-2,-3)$ and $(-3,5)$

(v) $(p, q)$ and $(r, s)$

(vi) $(2,3)$ and $(-1,-3)$

(vii) $(3,2)$ and $(2,5)$

Question 2

Find the equation of the circle, the end points of whose diameter are $(2,-3)$ and $(-2,4)$ Find its center and radius.

Question 3

Find the equation of the circle drawn on the intercept between the axes made by the line $3 x+4 y=12$ as a diameter.

Question 4

Show that equation of the circle passing through the origin and cutting intercepts $a$ and $b$ on the coordinate axes is $x^{2}+y^{2}-a x-b y=0$.

Question 5

Find the equation of the circle the end points of whose diameter are the centers of the circles :

$x^{2}+y^{2}+6 x-14 y=1 \text { and } x^{2}+y^{2}-4 x+10 y=2 \text {. }$

Question 6

The abscissa of two points $A$ and $B$ are the roots of the equation $x^{2}+2 x-a^{2}=0$ and the ordinates are the roots of the equation $y^{2}+4 y-b^{2}=0$. Find the equation of the circle with $A B$ as its diameter. Also find the coordinates of the center and the length of the radius of the circle.

Question 7

If $(4,1)$ be an end of a diameter of the circle $x^{2}+y^{2}-2 x+6 y-15=0$, find the coordinates of the other end of the diameter.

Type 2

Question 8

Find the equation of the circle drawn on a diagonal of the rectangle as is diameter whose sides are :

(i) $x=4, x=-2, y=5, y=-2$

(ii) $x=5, x=8, y=4, y=1$

Page no 22.37

Question 9

The sides of a square are $x=6, x=9, y=3$ and $y=6$ Find the equation of $z$ circle drawn on the diagonal of the square as its diameter.

Question 10

Find the equation of the circle circumscribing the rectangle whose sides are :

(i) $x=4, x=-5, y=5, y=-3$

(ii) $x=6, x=-3, y=3, y=-1$

(iii) $x-3 y=4,3 x+y=22, x-3 y=14,3 x+y=62$