7/2 x² + bxy + ry² = 0 | Find the value of r | Pair Of Straight Lines | SciPiPupil

Question: Find the value of r if the lines represented by the following equations are perpendicular to each other: $\frac{7}{2}x² + bxy +ry² = 0.

Solution:

Single equation of straight lines is $\frac{7}{2}x² + bxy +ry² = 0$ - (i)

Comparing equation (i) with $ax² + 2hxy + by² = 0$

$a = \frac{7}{2} \; and \; b = r$

Given, two lines represented by the above equation are perpendicular to each other then,

$a + b = 0$

$or, \dfrac{7}{2} + r = 0$

$\therefore r = - \dfrac{7}{2}$

Hence, the required value of r in the above equation is $- \frac{7}{2}$.