The two tangents to a circle from an external point are always
Equal
Perpendicular to each other
Parallel to each other
None of these
If the straight line $ax + by = 2;a,b \ne 0$ touches the circle ${x^2} + {y^2} - 2x = 3$ and is normal to the circle ${x^2} + {y^2} - 4y = 6$, then the values of a and b are respectively
The straight line $x + 2y = 1$ meets the coordinate axes at $A$ and $B$. A circle is drawn through $A, B$ and the origin. Then the sum of perpendicular distances from $A$ and $B$ on the tangent to the circle at the origin is
If the length of tangent drawn from the point $(5, 3)$ to the circle ${x^2} + {y^2} + 2x + ky + 17 = 0$ be $7$, then $k$ =
A pair of tangents are drawn from the origin to the circle ${x^2} + {y^2} + 20(x + y) + 20 = 0$. The equation of the pair of tangents is
If ${c^2} > {a^2}(1 + {m^2}),$ then the line $y = mx + c$ will intersect the circle ${x^2} + {y^2} = {a^2}$