Question 5
The point on the curve y2 = x, where the tangent makes an angle of 𝜋/4 with x-axis is
(A) (1/2, 1/4) (B) (1/4, 1/2)
(C) (4, 2) (D) (1, 1)
𝑦^2=𝑥
Slope of the tangent is 𝒅𝒚/𝒅𝒙
Finding 𝒅𝒚/𝒅𝒙
2y 𝑑𝑦/𝑑𝑥=1
𝒅𝒚/𝒅𝒙=𝟏/𝟐𝒚
Since, the tangent makes an angle of 𝜋/4 with x-axis
i.e., 𝜽=𝝅/𝟒
∴ Slope of tangent =𝒕𝒂𝒏 𝜽
=tan〖𝜋/4〗
=𝟏
Equating (1) and (2)
𝟏/𝟐𝒚=𝟏
1=2𝑦
2𝑦=1
𝒚=𝟏/𝟐
Since, we have to find point on the curve where the tangent makes an angle of 𝜋/4 with x-axis
Finding 𝒙 by putting 𝒚=𝟏/𝟐 in equation of curve
𝒚^𝟐=𝒙
(𝟏/𝟐)^2=𝑥
1/4 =𝑥
𝒙=𝟏/𝟒
∴ Required point = (x, y) = (𝟏/𝟒,𝟏/𝟐).
So, the correct answer is (B)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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