If the ratio of the lengths of tangents from a point to the circles $x^{2} + y^{2} + 4 x + 3$ = 0, $x^{2} + y^{2} - 6 x + 5$ = 0 is 1:2 then the locus of P is a circle whose centre is

Find the equation of family of circles through the intersection of $x^{2} + y^{2} - 6 x + 2 y + 4 = 0$ and $x^{2} + y^{2} + 2 x - 4 y - 6 = 0$ whose center lies on $y = x .$

Q. The locus of the mid point of the chord of the circle

x^{2} + y^{2} - 2 x - 2 y - 2 = 0

which makes an angle of

120^{0}

at the centre is.

Join BYJU'S Learning Program

A(−4,0) is a given point and B is a point on the locus x2+y2+5x−5=0. Find the equation of the locus of a point which divides seg. AB internally in the ratio 1:2

The correct option is A x2+y2+7x+11=0h=(−4)(2)+a(1)33b+8=ak=2(0)+b3⇒b=3kSince (a,b) lie on x2+y2+5x−5=0(3h+8)2+(3k)2+5(3h+8)−5=09h2+64+48h+9k2+15h+40−5=09h2+9k2+63h+99=0h2+k2+7h+11=0x2+y2+7x+11=0

$A (- 4, 0)$ is a given point and $B$ is a point on the locus $x^{2} + y^{2} + 5 x - 5 = 0$ . Find the equation of the locus of a point which divides seg. $A B$ internally in the ratio $1 : 2$