D.P. GUPTA, Preetima Bajpai and, Sanjeev Kumar Jha Solutions for Chapter: Conic Sections, Exercise 1: Exercise 1

Double ordinates $AB$ of the parabola $y^2=4ax$ subtends an angle $\frac{\mathrm{\pi }}{2}$ at the vertex of the parabola then tangents drawn to parabola at $A$ and $B$ will intersect at

If latus rectum of an ellipse is half of its minor axis, then its eccentricity is

Equation of the chord of the hyperbola $25x^2-16y^2=400$ which is bisected at the point $(6,2)$ is

The equation of the tangents to the ellipse $9x^2+16y^2=144$ which passes through the point $\left(2,3\right)$ is

The eccentricity of the conjugate hyperbola to the hyperbola $x^2-3y^2=1$ is

The normal at the point $\left(a{t}_1^2, 2a{t}_1\right)$ to the parabola meets the parabola again in the point $\left(a{t}_2^2, 2a{t}_2\right),$ then

The eccentricity of the ellipse, if the distance between the foci is equal to the length of the latus rectum is

The foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}$ coincide, then value of $b^2$ is