"If the tangent to the curve, y = ex at a point (c, ec) and the normal to the parabola, y2 = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is ________ ."

Question

Accepted Answer

"For $y = {e^x}$

${{dy} \over {dx}} = {e^x}$

${\left. {{{dy} \over {dx}}} \right|_{x = c}} = {e^c}$

Tangent is $y - {e^c} = {e^c}(x - c)$

Put y = 0, x = c$-$1.........(i)

For y² = 4x

$$2y{{dy} \over {dx}} = 4 \Rightarrow {\left. {{{ - dx} \over {dy}}} \right|_{y = 2}} = - 1$$

Normal is $y - 2 = - 1(x - 1)$

Put y = 0, x = 3 ...........(ii)

From (i) and (ii); $c - 1$ = 3

$\Rightarrow$ c = 4"

If the tangent to the curve, y = e^x at a point (c, e^c) and the normal to the parabola, y² = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is ________ .

Solution

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If the tangent to the curve, y = ex at a point (c, ec) and the normal to the parabola, y2 = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is ________ .

Solution

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If the tangent to the curve, y = e^x at a point (c, e^c) and the normal to the parabola, y² = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is ________ .