Mathematics - Application of Derivative Question with Solution | TestHub

$\frac{x^2}{a}+\frac{y^2}{b}=1\dots (1);\frac{x^2}{a_1}+\frac{y^2}{b_1}=1\dots (2)$ (1)-(2) $\Rightarrow x^2\left(\frac{1}{a}-\frac{1}{a_1}\right)+y^2\left(\frac{1}{b}-\frac{1}{b_1}\right)=0\Rightarrow \frac{x^2\left(a_1-a\right)}{a_{1}a}=-\frac{y^2\left(b_1-b\right)}{b_{1}b}\dots$ Differentiating (1): $\frac{x}{a}+\frac{y{m}_1}{b}=0\Rightarrow m_1=\frac{-bx}{ay},m_2=\frac{-b_{1}x}{a_{1}y}$ $m_1{m}_2=\frac{b_{1}b{x}^2}{a{a}_1{y}^2}=-\left(\frac{b_1-b}{a_1-a}\right)=-1\Rightarrow a-b=a_1-b_1$