The pair of lines represented by 3ax^2+5xy+(a^2-2)y^2=0 are perpendicular to each other fo…

Question

The pair of lines represented by $3ax^2+5xy+(a^2-2)y^2=0$ are perpendicular to each other for:

Accepted Answer

For $Ax^2+2Hxy+By^2=0$ to represent perpendicular lines: $A+B=0$:
$$3a+a^2-2=0 \implies a^2+3a-2=0$$

This has two real roots: $a=\dfrac{-3\pm\sqrt{17}}2$.

Solutions · 1