Embibe Experts Solutions for Exercise 12: EXERCISE 13.5

If $e$ and $e^{\text{'}}$ be the eccentricities of a hyperbola and its conjugate, then $e^2+{\left(e^{\text{'}}\right)}^2$ is equal to

If the distance between the foci and the distance between the directrices of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ are in the ratio $3:2,$ then $a:b$ is $=$

Let $PQ$ be a latus rectum of the hyperbola $\frac{x^2}{a^2}-\frac{k^2}{b^2}=1$ and $O$ be the centre. If $\Delta OPQ$ is an equilateral triangle and $e$ is eccentricity of the hyperbola, then

The line $5x+12y+9=0$ touches the hyperbola $x^2-9y^2=9$ at the point

The equation $2x^2+3y^2-8x-18y+35=k$ represents 

The equation of a tangent to the hyperbola $16x^2-25y^2-96x+100y-356=0$, which makes an angle $\frac{\pi }{4}$ with the transverse axis, is

The locus of a point $P\left(\alpha ,\beta \right)$ moving under the condition that the line $y=\alpha x+\beta$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, is

If $x=9$ is the chord of contact of the hyperbola $x^2-y^2=9,$ then the equation of the corresponding pair of tangents is -