AP EAPCET 25-Aug-2021 Shift 2 Paper

Standard form of ellipse,

x2

a2

+

y2

b2

=1 ...(i)
a > b
∵ Distance between foci =2ae
2=2ae ⇒ ae = 1
and length of latusrectum =

2b2

a

15

2

=

2b2

a

⇒b2=

15a

4

∵ b2=a2(−e2+1)=−a2e2+a2

15a

4

=−1+a2
⇒ 4a2−15a−4=0
4a2−16a+a−4=0
4a(a−4)+(a−4)=0
(4a+1)(a−4)=0
⇒ a=−

1

4

and 4
When, a=+4
⇒ b2=

15a

4

=

15×4

4

⇒b=√15
∴ Equation of ellipse,

x2

16

+

y2

15

=1
⇒ 15x2+16y2=240