The length intercepted by the curve $y^{2} = 4x$ on the line satisfying $dy/dx = 1$ and passing through point (0, 1), is given by

Question

Dr. Abubacker · Accepted Answer

(c)
Given curve is $y^{2} = 4x$ …(i)
Let the equation of line be $y = mx + c$
Since, $\frac{dy}{dx} = m = 1$ and above line is passing through the point (0, 1)
$1 = 1(0) + c\  \Rightarrow \ c = 1$
$y = x + 1$ …(ii)
On solving Eqs. (i) and (ii), we get
$x = 1$ and $y = 2$
This shows that line touch the curve at one point. So, length of intercept is zero.

Q. The length intercepted by the curve $y^{2} = 4x$ on the line satisfying $dy/dx = 1$ and passing through point (0, 1), is given by

Explanation

Reviewed by Dr. Abubacker

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