The chord of contact of the tangents drawn from a point on the circle $x^2 + y^2 = a^2$ to the circle $x^2 + y^2 = b^2$ touches the circle $x^2 + y^2 = c^2$. Then $a, b, c$ are in:

The equation of the common tangent to the parabola $y^2=8x$ and the circle $x^2+y^2=2$ is $ax+by+2=0$. If $-\frac{a}{b} > 0$,then $3a^2+2b+1=$

In a right triangle $ABC$,right-angled at $A$,a semicircle is described on the leg $AC$ as diameter. If $D$ is the point of intersection of the hypotenuse $BC$ and the semicircle,then the length $AC$ is equal to:

Given: $A$ circle $2x^2 + 2y^2 = 5$ and a parabola $y^2 = 4\sqrt{5}x$.
Statement-$1$: An equation of a common tangent to these curves is $y = x + \sqrt{5}$.
Statement-$2$: If the line $y = mx + \frac{\sqrt{5}}{m} (m \neq 0)$ is their common tangent,then $m$ satisfies $m^4 - 3m^2 + 2 = 0$.

Consider two curves $C_1 : y^2 = 2x$ and $C_2 : x^2 + y^2 - 3x + 2 = 0$. Then,

The area of the triangle formed by joining the origin to the points of intersection of the line $x\sqrt{5} + 2y = 3\sqrt{5}$ and the circle $x^2 + y^2 = 10$ is