Question

The line 3x - 2y = 0 coincides with one of the lines given by ax² + 2hxy + by² = 0, then ______

विकल्प

• 4a + 12h + 9b = 0

• 4a + 12h - 9b = 0

• 3a + 4h + 7b = 0

• 3a + 4h - 7b = 0

Answer 1

The line 3x - 2y = 0 coincides with one of the lines given by ax² + 2hxy + by² = 0, then 4a + 12h + 9b = 0.

Explanation:

The auxiliary form of equation ax² + 2hxy + by² = 0 is bm² + 2hm + a = 0.

The slope of line 3x - 2y = 0 is m = ${\displaystyle \frac{3}{2}}$.

3x - 2y = 0 coincides with one of the lines given by ax² + 2hxy + by² = 0.

∴ Substituting m = ${\displaystyle \frac{3}{2}}$ in auxiliary equation,

we get

${\displaystyle b{\left(\frac{3}{2}\right)}^2+2h\left(\frac{3}{2}\right)+a=0}$

⇒ 4a + 12h + 9b = 0