Question

D.E. whose solution is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ :

• A. $xy{y}_2+x{y}_1^2=y{y}_1$
• B. $xy{y}_2+y_1=y$
• C. $x^2{y}_2+x{y}_1=y$
• D. $x^2{y}_2+2x{y}_1=y_1^2$

Answer 1

The correct option is A $xy{y}_2+x{y}_1^2=y{y}_1$

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$\Rightarrow \frac{2x}{a^2}+\frac{2y{y}_1}{b^2}=0$

$\Rightarrow \frac{b^2}{a^2}=\frac{-y{y}_1}{x}$

$\Rightarrow \frac{1}{a^2}+\frac{1}{b^2}[y_1^2+y{y}_2]=0$

$\Rightarrow -\frac{b^2}{a^2}=y_1^2+y{y}_2$

$\Rightarrow y_1^2+y{y}_2=\frac{y{y}_1}{x}$

$\Rightarrow xy{y}_2+x{y}_1^2=y{y}_1$