The equation of the chord of the circle ${x^2} + {y^2} = {a^2}$ having $({x_1},{y_1})$ as its mid-point is
$x{y_1} + y{x_1} = {a^2}$
${x_1} + {y_1} = a$
$x{x_1} + y{y_1} = x_1^2 + y_1^2$
$x{x_1} + y{y_1} = {a^2}$
Equation of the pair of tangents drawn from the origin to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is
The equation of the tangents to the circle ${x^2} + {y^2} + 4x - 4y + 4 = 0$ which make equal intercepts on the positive coordinate axes is given by
Tangents are drawn from the point $(4, 3)$ to the circle ${x^2} + {y^2} = 9$. The area of the triangle formed by them and the line joining their points of contact is
The gradient of the tangent line at the point $(a\cos \alpha ,a\sin \alpha )$ to the circle ${x^2} + {y^2} = {a^2}$, is
Two tangents are drawn from the point $\mathrm{P}(-1,1)$ to the circle $\mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}-6 \mathrm{y}+6=0$. If these tangents touch the circle at points $A$ and $B$, and if $D$ is a point on the circle such that length of the segments $A B$ and $A D$ are equal, then the area of the triangle $A B D$ is eqaul to: