AP EAPCET 19-Aug-2021 Shift 2 Paper

Given curves,

x2

a2

+

y2

4

=1 ...(i)
and y3=16x ...(ii)
Differentiating Eq. (i) w.r.t. x

2x

a2

+

y

2

dy

dx

=0
⇒

dy

dx

=

−4x

a2y

=m1 (let)
Differentiating Eq. (ii) w.r.t. x
3y2

dy

dx

=16
⇒

dy

dx

=

16

3y2

=m2 (let)
∵ Eqs. (i) and (ii) meet each other at right angles
m1m2=−1
⇒

16

3y2

.

−4x

a2y

=−1
⇒64x=3a2y3
⇒a2=

64x

3y3

⇒a2=

64x

3×16x

‌‌‌‌‌‌ [as y3=16x]
⇒a2=

4

3