Question

decode it akm is for pros​

Answer 1

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Answer 2

SOLUTION

The given equation of the curve is:

=) √x +√y=4............(1)

On differentiating with respect to x

$= > \frac{1}{2} x {}^{ \frac{ - 1}{2} } + \frac{1}{2} y {}^{ \frac{ - 1}{2} } \frac{dy}{dx} = 0 \\ = > \frac{1}{ \sqrt{y} } \frac{dy}{dx} = \frac{ - 1}{ \sqrt{x} } \\ = > \frac{dy}{dx} = \frac{ - \sqrt{ y} }{ \sqrt{x} } ..............(2)$

Since the tangent to the curve is equally inclined to the coordinate are:

$= > \frac{dy}{dx} = tan(145) \: m = tan \theta = \frac{dy}{dx} \\ = > \frac{dy}{dx} = </u></strong><strong><u>±</u></strong><strong><u>1 \\ = > \frac{ - \sqrt{y} }{ \sqrt{x} } = </u></strong><strong><u>±</u></strong><strong><u>1 \\ = > \sqrt{y} = </u></strong><strong><u>±</u></strong><strong><u> \sqrt{x} \\ = > y = x................(3)$

Put the value of y= x in eq. (1), we get

=) √x + √x= 4

=) 2√x= 4 , x= 4

=) √x= 2 , y= 4

hope it helps ☺️