A tangent to the circle ${x^2} + {y^2} = 5$at the point $(1,-2)$ the circle ${x^2} + {y^2} - 8x + 6y + 20 = 0$
Touches
Cuts at real points
Cuts at imaginary points
None of these
The normal at the point $(3, 4)$ on a circle cuts the circle at the point $(-1, -2)$. Then the equation of the circle is
Two tangents drawn from the origin to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ will be perpendicular to each other, if
In the figure, $A B C D$ is a unit square. A circle is drawn with centre $O$ on the extended line $C D$ and passing through $A$. If the diagonal $A C$ is tangent to the circle, then the area of the shaded region is
The slope of the tangent at the point $(h,h)$ of the circle ${x^2} + {y^2} = {a^2}$ is
If the line $3x -4y -k = 0 (k > 0)$ touches the circle $x^2 + y^2 -4x -8y -5 = 0$ at $(a, b)$ then $k + a + b$ is equal to :-