G Tewani Solutions for Chapter: Hyperbola, Exercise 3: DPP

The equation of a hyperbola whose asymptotes are $3x\pm 5y=0$ and vertices are $\left(\pm 5, 0\right)$, is

The tangent at $P$ on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ meets one of the asymptotes in $Q$. Then, the locus of the mid-point of $PQ$ is

The locus of a perpendicular from the center upon the normal to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is

Let the transverse axis of a varying hyperbola be fixed with the length of the transverse axis being $2a$. Then, the locus of the point of contact of any tangent drawn to it from a fixed point on the conjugate axis is

The locus of the foot of the perpendicular from the center of the hyperbola $xy=c^2$ on a variable tangent is

If two tangents can be drawn to the different branches of a hyperbola $\frac{x^2}{1}-\frac{y^2}{4}=1$ from $\left(\alpha , {\alpha }^2\right),$ then

The director circle of a hyperbola is $x^2+y^2-4y=0$. If one end of the major axis is at $\left(2, 0\right)$, then the focus is

The points on the ellipse $\frac{x^2}{2}+\frac{y^2}{10}=1$ from which the perpendicular tangents can be drawn to the hyperbola $\frac{x^2}{5}-\frac{y^2}{1}=1$ are