Position of a point with respect to Hyperbola - Practice Questions & MCQ

Let $a$ and $b$ be the semi-transverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation $9 e^2-18 e+5=0$. If $S(5,0)$ is a focus and $5 x=9$ is the corresponding directrix of this hyperbola, then $\mathrm{a}^2-\mathrm{b}^2$ is equal to :

The foci of a hyperbola coincide with the foci of ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$. If the eccentricity of the hyperbola is 3, then its equation is

If the polar of a point w.r.t.  touches the hyperbola , then the locus of the point is:

The locus of the poles of the chords of the hyperbola , which subtend a right angle at the centre is:

Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is

$
\text { The value of } \alpha \text { such that } \alpha(2 \alpha, 3 \alpha) \text { lies inside the hyperbola } \frac{x^2}{16}-\frac{y^2}{9}=1 \text {, lies in the interval }
$

The line $25 \mathrm{x}+12 \mathrm{y}-45=0$ meets the hyperbola $25 \mathrm{x}^2-9 \mathrm{y}^2=225$ only at point $\left(5,-\frac{5 \mathrm{k}}{3}\right)$, then the value of k is