On a circle with centre `(2, 1)` and radius `3`, a variable point A is taken such that perpendiculars from `A` on a diameter (not containing A) of circle are divided by a point `B` in fixed ratio `1:3`. Then find the locus of `B`.

If the line joining A(1,3,4) and B is divided by the point (-2,3,5) in the ratio 1:3 then the coordinates of B is

A line perpendicular to the in segment joining the points (1,0) and (2,3) divides it in the ratio 1: n . Find the equation of the line.

Find the equation of the circle with centre (−a,−b) and radius sqrt(a^2 −b^2) ​

Find the equation of the circle with centre : (-a , b) and radius sqrt(a^2-b^2) .

Make a point P and draw a circle with centre P and radius 5 cm. Take any point Q on the circle drawn. With Q as centre and radius 3 cm draw another circle. Label the two points at which the circles intersect as A and B. Join PQ and AB. Find the angle between AB and PQ.

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

A (2, 3) is a fixed point and Q(3 cos theta, 2 sin theta) a variable point. If P divides AQ internally in the ratio 3:1, find the locus of P.

A B is a diameter of a circle with centre O and radius O D is perpendicular to A B . If C is any point on arc D B , find /_B A D\ a n d\ /_A C D .

If A(2,-1)a n dB(6,5) are two points, then find the ratio in which the food of the perpendicular from (4,1) to A B divides it.

If A(2,-1)a n dB(6,5) are two points, then find the ratio in which the food of the perpendicular from (4,1) to A B divides it.