Question 42 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at May 29, 2023 by Teachoo

For which value of m is the line y = mx + 1 a tangent to the curve y
^{
2
}
= 4x?

Question 42 For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x? (a) 1/2 (b) 1 (c) 2 (d) 3
Let (ℎ , 𝑘) be the point at which tangent is to be taken
Since (𝒉 , 𝒌) lies on line
𝑘=𝑚ℎ+1
Since (𝒉 , 𝒌) lies on curve
𝑘^2=4ℎ
ℎ=𝑘^2/4
Putting (2) in (1)
𝑘=𝑚(𝒌^𝟐/𝟒)+1
4𝑘=𝑚𝑘^2+4
𝑚𝑘^2−4𝑘+4=0
Since tangent touches the curve at only one point
There is only one value of k
So, this quadratic equation has only one root
Thus,
Discriminant of Quadratic equation = 0
𝒃^𝟐−𝟒𝒂𝒄=𝟎
(−4)^2−4 × 𝑚 × 4=0
16−16𝑚=0
𝑚=16/16
𝒎=𝟏
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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