KCET 2015 Math Solved Paper

Given equation of hyperbola,

x2

a2

−

y2

b2

=1 → (1)
and a focal chord of the hyperbola is,
2x+3y−6=0 → (2)
We know that, focus is given by (ae, 0). So, from Eq. (2) we have
2ae−6=0⇒ae=3⇒a=‌

3

e

Hence e=

5

4

then,
⇒a=‌

3

5∕4

=‌

12

5

Length of the transverse axis is 2a. So,2a=‌

24

5