Dr. SK Goyal Solutions for Chapter: Hyperbola, Exercise 6: Multiple Choice I

Tangents are drawn from a point on the circle $x^2+y^2=11$ to the hyperbola $\frac{x^2}{36}-\frac{y^2}{25}=1$, then tangents are at angle:

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

Consider the set of hyperbola $xy=k,k\in R$. Let $e_1$ be the eccentricity when $k=4$ and $e_2$ be the eccentricity when $k=9$ then $e_1-e_2=$

Equation of the hyperbola passing through the point $\left(1,-1\right)$ and having asymptotes $x+2y+3=0$ and $3x+4y+5=0$ is:

The eccentricity of the conic $4{\left(2y-x-3\right)}^2-9{\left(2x+y-1\right)}^2=80$ is:

The point of intersection of the curves whose parametric equations are $x=t^2+1,y=2t$ and $x=2s, y=\frac{2}{s}$  is given by -

If a triangle is inscribed in a rectangular hyperbola, its orthocentre lies:

If the tangent and normal to a rectangular hyperbola cut off intercepts $x_1$ and $x_2$ on one axis and $y_1$ and $y_2$ on the other axis, then: