Q

The line y is equal to m x plus 1 is a tangent to the curve y raised to 2 is equal to 4x if the value of m is (A) 1 (B) 2 (C) 3 (D) 1 2

21) The line y is equal to  $mx+1$ is a tangent to the curve $y^2 = 4x$if the value of m is
(A) 1

(B) 2

(C) 3

(D)1/2

Views

Standard equation of the straight line
y = mx + c
Where m is lope and c is constant
By comparing it with equation , y = mx + 1
We find that m is the slope
Now,
we know that the slope of the tangent at a given point on the curve is given by $\frac{dy}{dx}$
Given the equation of the curve is
$y^2 = 4x$
$2y\frac{dy}{dx} = 4\\ \frac{dy}{dx} = \frac{2}{y}$
Put this value of m in the given equation
$y = \frac{2}{y}.\frac{y^2}{4}+1 \ \ \ \ \ \ \ \ \ \ (\because y^2 = 4x \ and \ m =\frac{2}{y})\\ y = \frac{y}{2}+1\\ \frac{y}{2} = 1\\ y = 2$
$m = \frac{2}{y} = \frac{2}{2} = 1$
Hence, value of m is 1