IPMAT Indore (MCQ) PYQs

Which of the following straight lines are both tangent to the circle $x ^ 2 + y ^ 2 - 6x + 4y - 12 = 0$?

If $\theta$ is the angle between the pair of tangents drawn from the point $(0,\frac{7}{2})$ to the circle $x^2 + y^2 - 14x + 16y + 88 = 0$, then $\tan \theta$ equals

The circle $x^2 + y^2 - 6x - 10y + k = 0$ does not touch or intersect the coordinate axes. If the point $(1, 4)$ does not lie outside the circle, and the range of $k$ is $(a, b]$, then $a + b$ is