Question

Two curves $a_i{x}^2+b_i{y}^2=1;i=1,2$ where, $a_1\ne a_2,b_1\ne b_2,a_1,a_2,b_1,b_2\ne 0$ may intersect orthogonally if __________.

• A. $a_1{a}_2=b_1{b}_2$
• B. $a_1^{-1}-a_2^{-1}=b_1^{-1}-b_2^{-1}$
• C. $a_1^{-1}+a_2^{-1}=b_1^{-1}+b_2^{-1}$
• D. $a_1{b}_2=a_2{b}_1$

Answer 1

Answer: (B)

$a_1^{-1}-a_2^{-1}=b_1^{-1}-b_2^{-1}$

Two curves $a_i{x}^2+b_i{y}^2=1;i=1,2$ where, $a_1\ne a_2,b_1\ne b_2,a_1,a_2,b_1,b_2\ne 0$

If $a_1{x}^2+b_1{y}^2=1$ and $a_2{x}^2+b_2{y}^2=1$ are orthogonal to each other then,

$\frac{1}{a_1}-\frac{1}{a_2}=\frac{1}{b_1}-\frac{1}{b^2}$.

$\Rightarrow a_1^{-1}-a_2^{-1}=b_1^{-1}-b_2^{-1}$