Question:

The line y=mx+1y = mx + 1 is a tangent to the curve y2=4xy^2 = 4x if the value of mm is

Updated On: Sep 15, 2023
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The Correct Option is A

Solution and Explanation

The correct answer is A:1
The equation of the tangent to the given curve is y=mx+1y = mx + 1. Now, substituting y=mx+1y = mx + 1 in y2=4xy^2 = 4x, we get:
(mx+1)2=4x(mx+1)^2=4x
m2x2+1+2mx4x=0m^2x^2+1+2mx-4x=0
m2x2+x(2m4)+1=0...(i)m^2x^2+x(2m-4)+1=0 ...(i)
Since a tangent touches the curve at one point, the roots of equation (i) must be equal. Therefore, we have:
Discriminant=0
(2m4)24(m2)(1)=0(2m-4)^2-4(m^2)(1)=0
=4m2+1616m4m2=0=4m^2+16-16m-4m^2=0
1616m=016-16m=0
m=1m=1
Hence, the required value of m is 1.
The correct answer is A
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