UPSEE Solved Model Paper 1

The equation of any tangents of slope m to the parabola y2 = 4x is
𝑦 = 𝑚𝑥 +

1

m

... (i)
If it passes through P(1,4), then
4 = m+

1

m

⇒ m2 - 4m + 1 = 0
Let m1,m2 be the roots of this equation, Then, ma + m2 = 4 and m1m2= 1
Let e be the angle between the tangents drawn from P.
Then,
tan𝜃 =

m1−m2

1+m1m2

=

√(m1+m2)2−4m1m2

1+m1m2

⇒ tan θ =

√16−4

2

= √3
⇒ θ =

π

3