Length of the tangent from $({x_1},{y_1})$ to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is
${(x_1^2 + y_1^2 + 2g{x_1} + 2f{y_1} + c)^{1/2}}$
${(x_1^2 + y_1^2)^{1/2}}$
${[{({x_1} + g)^2} + {({y_1} + f)^2}]^{1/2}}$
None of these
Let $y=x+2,4 y=3 x+6$ and $3 y=4 x+1$ be three tangent lines to the circle $(x-h)^2+(y-k)^2=r^2$. Then $h+k$ is equal to :
The line $2x - y + 1 = 0$ is tangent to the circle at the point $(2, 5)$ and the centre of the circles lies on $x-2y=4$. The radius of the circle is
At which point on $y$-axis the line $x = 0$ is a tangent to circle ${x^2} + {y^2} - 2x - 6y + 9 = 0$
Consider circle $S$ : $x^2 + y^2 = 1$ and $P(0, -1)$ on it. $A$ ray of light gets reflected from tangent to $S$ at $P$ from the point with abscissa $-3$ and becomes tangent to the circle $S.$ Equation of reflected ray is
Given the circles ${x^2} + {y^2} - 4x - 5 = 0$and ${x^2} + {y^2} + 6x - 2y + 6 = 0$. Let $P$ be a point $(\alpha ,\beta )$such that the tangents from P to both the circles are equal, then