Let PA and PB be the tangent segments drawn from point P$(6, 8)$ to the circle with the centre at origin O. The radius of circle for which the area of quadrilateral PAOB is maximum, is...

A circle passes through the point $(0,1)$ and touches the parabola $y = x^2$ at the point $(1,1)$. The centre of the circle is...

The eccentricity of the ellipse represented by the equation $7x^2 + 16y^2 - 14x + 64y - 377 = 0$ is...

If $\lim_{x \to 1} \dfrac{x^3 + ax^2 + bx + c}{x^2 - 2x + 1} = 2026$ then the value of $a - c$ is...