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

(B) 2

(C) 3

(D)1/2

Answers (1)

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
Hence, (A) is correct  answer

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