JEE 2022 — Mathematics PYQ

1. Use the Axis Sum Equation

The transverse axis is $2a$ and the conjugate axis is $2b$.

2. Use the Eccentricity to find the ratio of $b$ to $a$

Given $e=\frac{\sqrt{11}}{2}$.

For a hyperbola, $e^2=1+\frac{b^2}{a^2}$.

Taking the square root (since a, b > 0):

3. Substitute $b$ into the sum equation

Divide both sides by $(2+\sqrt{7})$:

4. Calculate $a^2$ and $b^2$

• $a^2=(4\sqrt{2}{)}^2=16\times 2=32$

• $b^2=\frac{7}{4}{a}^2=\frac{7}{4}(32)=7\times 8=56$

5. Find the final value

The question asks for $a^2+b^2$ (Let's check if the "2" in the previous prompt was a typo in the request):

• $a^2+b^2=32+56=88$