EXERCISE-1

Pair of tangents are drawn from every point on the line $3x+4y=12$ on the circle $x^2+y^2=4$. Their variable chord of contact always passes through a fixed point whose co-ordinates are

The locus of the mid-points of the chords of the circle $x^2+y^2-2x-4y-11=0$ which subtend $60°$ at the centre is

A circle is drawn touching the $x$-axis and centre at the point which is the reflection of $\left(a,b\right)$ in the line $y-x=0$. The equation of the circle is

If the two circles, $x^2+y^2+2g_{1}x+2f_{1}y=0$ and $x^2+y^2+2g_{2}x+2f_{2}y=0$ touches each other, then

The tangent from the point of intersection of the lines $2x-3y+1=0$ and $3x-2y-1=0$ to the circle $x^2+y^2+2x-4y=0$ is

The length of the common chord of circles $x^2+y^2-6x-16=0$ and $x^2+y^2-8y-9=0$ is

The number of common tangents of the circles $x^2+y^2-2x-1=0$ and $x^2+y^2-2y-7=0$

If the circle $x^2+y^2=9$ touches the circle $x^2+y^2+6y+c=0$, then $c$ is equal to