INTRODUCTORY EXERCISE 7.1

The eccentricity of the conic represented by $x^2-y^2-4x+4y+16=0$ is

The eccentricity of the hyperbola whose latus rectum is $8$ and conjugate axis is equal to half the distance between the foci is 

The equation $\frac{x^2}{10-\lambda }+\frac{y^2}{6-\lambda }=1$ represents :

Find the equation of the hyperbola whose foci are at $(\pm 3\sqrt{10}, 0)$ and passes through the point $(-9, 0).$

Find the equation of the hyperbola whose foci at $(\pm 2,0)$ and eccentricity is $\frac{3}{2}$.

Find the centre, eccentricity and length of axes of the hyperbola
$3x^2-5y^2-6x+20y-32=0$

Find the eccentricity of the conjugate hyperbola $x^2-3y^2=1$.

Find the equation of tangent to the parabola $y^2=16x$ which is parallel to the line $3x-4y+5=0$. Also find the point of contact.