Embibe Experts Solutions for Chapter: Hyperbola, Exercise 3: EXERCISE-3

The hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\left(a, b>0\right)$ passes through the point of intersection of the lines, $7x+13y-87=0$ and $5x-8y+7=0$ and the latus rectum is $\frac{32\sqrt{2}}{5},$ then value of $b$ is equal to

 If eccentricity of the hyperbola whose latus rectum is half its transverse axis is $\sqrt{\lambda },$ then $\lambda$ is equal to

For the hyperbola $\frac{x^2}{100}-\frac{y^2}{25}=1,$ then value of $\sqrt{SA\times S\text{'}A}$ is equal to, (where $S$ and $S\text{'}$ are the foci  and $A$ is the vertex of the hyperbola)

If eccentricity of the conic represented by $x^2-y^2-4x+4y+16=0$ is $\sqrt{\lambda },$ then $\lambda$ is equal to

Value of $\left|\lambda \right|$ when the line $y=3x+\lambda$ touch the hyperbola $9x^2-5y^2=45$ is