4x² -12xy +9y² = 0 | Prove that the lines represented by the following equation is coincident. | Pair Of Straight Lines | SciPiPupil

Question: Prove that the lines represented by the following equation is coincident: $4x² -12xy +9y² = 0$.

Solution:

Given,

Equation of line is $4x² -12xy +9y² = 0$

$or, 4x² - 2×6xy + 9y² = 0$ - (i)

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

$a = 4, h = -6, and b = 9$

We know, when two lines are coincident, $h² = ab$,

$or, h² = ab$

$or, (-6)² = 4×9$

$or, 36 = 36$ which is true.

Therefore, it is proved that the lines represented by the given equation is coincident.

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