Which of the following points lies on the tangent to

Question:

Which of the following points lies on the tangent to the curve $x^{4} e^{y}+2 \sqrt{y+1}=3$ at the

point $(1,0)$ ?

  1. $(2,2)$

  2. $(-2,6)$

  3. $(-2,4)$

  4. $(2,6)$


Correct Option: , 2

Solution:

$x^{4} e^{y}+2 \sqrt{y+1}=3$

d.W.r. to $\mathrm{X}$

$x^{4} e^{y} y^{\prime}+e^{y} 4 x^{3}+\frac{2 y^{\prime}}{2 \sqrt{y+1}}=0$

at $\mathrm{P}(1,0)$

$y_{P}^{\prime}+4+y_{P}^{\prime}=0$

$\Rightarrow y_{P}^{\prime}=-2$

Tangent at $\mathrm{P}(1,0)$ is

$y-0=-2(x-1)$

$2 x+y-2$

$(-2,6)$ lies on it

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