Embibe Experts Solutions for Exercise 3: EXERCISE 12.3

Area of quadrilateral formed by a pair of tangents from the point $(4, 5)$ to the circle $x^2+y^2-4x-2y-11=0$ and a pair of its radii is

Equation of chord of the circle $x^2+y^2+6x+8y-11=0$ whose middle point is $(1, -1)$ is

Tangents are drawn to the circle $x^2+y^2=16$ at the points where it is met by the circle $x^2+y^2-5x+3y-2=0$ the point of intersection of these tangents is

A circle cutting the circle $x^2+y^2=4$ orthogonally and having its centre on the line $2x-2y+9=0,$ passes through two fixed points. These points are

Consider three circles $x^2+y^2=1, x^2+y^2-8x+15=0, x^2+y^2+10y+24=0.$ The point from which tangents of equal length can be drawn to all these three circles is

Interval of $r$ for which $x^2+y^2=r^2$and $x^2+y^2-6x-8y+9=0$ cut at two distinct points is

Number of common real tangents that can be drawn to the circles $x^2+y^2-2x-2y=0$ and $x^2+y^2-8x-8y+14=0$ is

The equation of a chord of the circle $x^2+y^2+4x-6y=0$ is given by $x+2y=0.$ The equation of the circle described on this chord as diameter is