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
${x^2} + {y^2} + 10xy = 0$
${x^2} + {y^2} + 5xy = 0$
$2{x^2} + 2{y^2} + 5xy = 0$
$2{x^2} + 2{y^2} - 5xy = 0$
The length of tangent from the point $(5, 1)$ to the circle ${x^2} + {y^2} + 6x - 4y - 3 = 0$, is
The line $y = mx + c$ will be a normal to the circle with radius $r$ and centre at $(a, b)$, if
Tangent to the circle $x^2 + y^2$ = $5$ at the point $(1, -2)$ also touches the circle $x^2 + y^2 -8x + 6y + 20$ = $0$ . Then its point of contact is
The tangent at $P$, any point on the circle ${x^2} + {y^2} = 4$, meets the coordinate axes in $A$ and $B$, then
The line $ax + by + c = 0$ is a normal to the circle ${x^2} + {y^2} = {r^2}$. The portion of the line $ax + by + c = 0$ intercepted by this circle is of length