The correct option is C a2=252
The point of intersection of 7x+13y−87=0 and 5x−8y+7=0 is (5,4)
Also 2b2a=32√25
b2=16√25a2 (a>0,b>0)
So, x2a2−y2.516√2a=1
It will pass through (5,4)
25a2−16516√2a=1
⇒5a2−1√2a=15⇒5a2−1√2a−15=0
1a=12±√12+42.5=1±310√2
Take positive sign only
a=10√24
a2=252
and b2=16√25×5√2=16
b2=16