Question:
A tangent to the parabola y2 = 4x is inclined at an angle of 45° with the positive direction of x-axis. What is point of contact of the tangent and the parabola?
A tangent to the parabola y2 = 4x is inclined at an angle of 45° with the positive direction of x-axis. What is point of contact of the tangent and the parabola?
Options:
- a) (1, 1)
- b) (, )22
- c) 1 2 1 2 ,
- d) (1, 2)
- a) (1, 1)
- b) (, )22
- c) 1 2 1 2 ,
- d) (1, 2)
correct answer : d)
Explanation:
Scope of tangent = tan 45° = 1
y2 = 4x Þ
2y dy
dx
= 4
Þ
dy
dx
=
4
2y
= 1 Þ y = 2
putting in y2 = 4x Þ x = 1
\ Point of contact = (1, 2)
Scope of tangent = tan 45° = 1
y2 = 4x Þ
2y dy
dx
= 4
Þ
dy
dx
=
4
2y
= 1 Þ y = 2
putting in y2 = 4x Þ x = 1
\ Point of contact = (1, 2)