The line y = mx + 1 is a tangent to the curve y2 = 4x, if the value of m is

Q27 of 149 Page 16

The line y = mx + 1 is a tangent to the curve y² = 4x, if the value of m is

It is given that the line y = mx + 1 is a tangent to the curve y² = 4x.

Slope of the line = m

Slope of the curve

Differentiating the curve we get

∵ The given line is a tangent to the curve so the point passes through both line and curve.

⇒ 2 – m =1

⇒ m = 1

Hence, the correct option is A.

The point on the curve 9y² = x³, where the normal to the curve makes equal intercepts with the axes is

The slope of the tangent to the curve x = t² + 3t – 8, y = 2t² – 2t – 5 at the point (2, –1) is

The normal at the point (1, 1) on the curve 2y + x² = 3 is

The normal to the curve x² = 4y passing through (1, 2) is