COMEDK Exam 2015 Solved Paper

We have, y2=4ax . . . (i)
and ay=2x2 . . . (ii)
Solving Eqs. (i) and (ii), we get x=a and y=2a
Differentiating Eq. (i) w.r.t. x, we get
2y‌

dy

dx

=4a
Now, ‌‌[‌

dy

dx

](a,2a)=‌

4a

2(2a)

=1
⇒‌‌m1=1
Now, differentiating Eq. (ii) w.r.t. x, we get
‌a‌

dy

dx

=4x⇒[‌

dy

dx

](a,2a)=‌

4a

a

=4
⇒‌‌m2=4
∵ Angle between curves is equal to angle between their tangents.
tan‌θ‌|‌

m2−m1

1+m1m2

|⇒tan‌θ=|‌

4−1

1+4×(1)

|
⇒tan‌θ=‌

3

5

⇒θ=tan−1(‌

3

5

)