Equation of the pair of tangents drawn from the origin to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is
$gx + fy + c({x^2} + {y^2})$
${(gx + fy)^2} = {x^2} + {y^2}$
${(gx + fy)^2} = {c^2}({x^2} + {y^2})$
${(gx + fy)^2} = c({x^2} + {y^2})$
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
If variable point $(x, y)$ satisfies the equation $x^2 + y^2 -8x -6y + 9 = 0$ , then range of $\frac{y}{x}$ is
The number of tangents which can be drawn from the point $(-1,2)$ to the circle ${x^2} + {y^2} + 2x - 4y + 4 = 0$ is
The equation of the normal to the circle ${x^2} + {y^2} = 9$ at the point $\left( {\frac{1}{{\sqrt 2 }},\frac{1}{{\sqrt 2 }}} \right)$ is
If a circle $C$ passing through the point $(4, 0)$ touches the circle $x^2 + y^2 + 4x -6y = 12$ externally at the point $(1, -1)$, then the radius of $C$ is