Question

the line y=mx + 1 is a tangent to the curve y^2 =2x - 3 ,find the values of m

Answer 1

Lets put y=mx+1 in y

2

=4x we get

(mx+1)

2

=4x

⇒m

2

x

2

+1+2mx−4x=0

Tangent touches a curve at one point so descriminant of the equation should be zero.

⇒(2m−4)

2

−4×1×m

2

=0

⇒4m

2

+16−16m−4m

2

=0

⇒m=1