Circle

The equation of the circle with centre $(0,2)$ and radius 2 is $x^2+y^2-m y=0$. The value of $m$ is

The locus of the mid-point of the chord if contact of tangents drawn from points lying on the straight line $4 x-5 y=20$ to the circle $x^2+y^2=9$ is

For each parabola $y=x^2+p x+q$, meeting coordinate axes at 3-distinct points, if circles are drawn through these points, then the family of circles must pass through

If a chord of the circle $x^{2}+y^{2}=8$ makes equal intercets of length a on the coordinate axes, then

If two distinct chords drawn from the point $(p, q)$ on the circle ${x}^{2}+{y}^{2}=px+qy$ (where $pq≠0$) are bisected by the $X$-axis, then

The lengths of the tangent drawn from any point on the circle $15 x^{2}+15 y^{2}-48 x+64 y=0$ to the two circles $5 x^{2}+5 y^{2}-24 x+32 y+75=0$ and $5 x^{2}+5 y^{2}-48 x$ $+64 y+300=0$ are in the ratio of

The number of integral values of $\lambda$ for which $\mathrm{x}^{2}+\mathrm{y}^{2}+\lambda \mathrm{x}+(1-\lambda) \mathrm{y}+5=0$ is the equation of a ircle whose radius cannot exceed $5,$ is

The line joining (5,0) to $((10 \cos \theta, 10 \sin \theta)$ is divided internally in the ratio 2: 3 at $P$. If $\theta$ varies, then the locus of $\mathrm{P}$ is

The angle of intersection of the two circles $x^{2}+y^{2}-2 x-2 y=0$ and $x^{2}+y^{2}=4,$ is

A pair of tangents are drawn from the origin to the circle $x^{2}+y^{2}+20(x+y)+20=0,$ then the equation of the pair of tangent are

If the lines \(3 x-4 y+4=0\) and \(6 x-8 y-7=0\) are tangents to a circle, then the radius of the circle is

For what value of \(k\) the circles \(x^2+y^2+5 x+3 y+7=0\) and \(x^2+y^2-8 x+6 y+k=0\) cuts orthogonally