SATHEE: Straight Line and Pair of Straight Lines 1 Question 13

Straight Line and Pair of Straight Lines 1 Question 13

13. The tangent to the curve, $y = x e^{x^{2}}$ passing through the point $(1, e)$ also passes through the point

(2019 Main, 10 Jan II)

(a) $\frac{4}{3}, 2 e$

(b) $(3, 6 e)$

(d) $\frac{5}{3}, 2 e$

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Solution:

Given equation of curve is $y = x e^{x^{2}}$

Note that $(1, e)$ lie on the curve, so the point of contact is $(1, e)$ .

Now, slope of tangent, at point $(1, e)$ , to the curve (i) is

$\begin{aligned} {\frac{d y}{d x} |}_{(1, e)} & = x (2 x) e^{x^{2}} + e^{x^{2}} \\ = 2 e + e = 3 e \end{aligned}$

Now, equation of tangent is given by

$\begin{matrix} (y - y_{1}) = m (x - x_{1}) \\ y - e = 3 e (x - 1) \Rightarrow y = 3 e x - 2 e \end{matrix}$

On checking all the options, the option $\frac{4}{3}, 2 e$ satisfy the equation of tangent.

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Straight Line and Pair of Straight Lines 1 Question 13

13. The tangent to the curve, y=xex2 passing through the point (1,e) also passes through the point

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13. The tangent to the curve, $y = x e^{x^{2}}$ passing through the point $(1, e)$ also passes through the point