rx² + 5xy -6y² | 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: rx² + 5xy -6y² = 0.

Solution:

Single equation of straight lines is $rx² + 5xy -6y² = 0$ - (i)

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

$a = r \; and \; b = -6$

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

$a + b = 0$

$or, r -6 = 0$

$\therefore r = 6$

Hence, the required value of r in the above equation is 6.