If y-1-x2-x-1-y2-1 if dydx-m-1- y2-1-x2-Find m

On differentiating, we get y( 2x)2√(1 x^2)+(√(1 x^2))dydx+x2√(1 y^2)( 2y)dydx+√(1 y^2)=0 On solving further, we get dydx= √(1 y^21 x^2) Thus, we can say ...

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Byju's Answer

Standard XII

Mathematics

Variable Separable Method

If y√1-x2+x...

Question

If $y \sqrt{1 - x^{2}} + x \sqrt{1 - y^{2}} = 1$ if $\frac{d y}{d x} = - m \sqrt{\frac{1 - y^{2}}{1 - x^{2}}}$ .Find $m$

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Solution

On differentiating, we get
$\frac{y (- 2 x)}{2 \sqrt{1 - x^{2}}} + (\sqrt{1 - x^{2}}) \frac{d y}{d x} + \frac{x}{2 \sqrt{1 - y^{2}}} (- 2 y) \frac{d y}{d x} + \sqrt{1 - y^{2}} = 0$
On solving further, we get
$\frac{d y}{d x} = - \sqrt{\frac{1 - y^{2}}{1 - x^{2}}}$
Thus, we can say that $m = 1$ .

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If y√1−x2+x√1−y2=1 if dydx=−m√1−y21−x2.Find m

On differentiating, we gety(−2x)2√1−x2+(√1−x2)dydx+x2√1−y2(−2y)dydx+√1−y2=0On solving further, we getdydx=−√1−y21−x2Thus, we can say that m=1.

If $y \sqrt{1 - x^{2}} + x \sqrt{1 - y^{2}} = 1$ if $\frac{d y}{d x} = - m \sqrt{\frac{1 - y^{2}}{1 - x^{2}}}$ .Find $m$

On differentiating, we get
$\frac{y (- 2 x)}{2 \sqrt{1 - x^{2}}} + (\sqrt{1 - x^{2}}) \frac{d y}{d x} + \frac{x}{2 \sqrt{1 - y^{2}}} (- 2 y) \frac{d y}{d x} + \sqrt{1 - y^{2}} = 0$
On solving further, we get
$\frac{d y}{d x} = - \sqrt{\frac{1 - y^{2}}{1 - x^{2}}}$
Thus, we can say that $m = 1$ .