2x² +12xy + 18y² = 0 | Prove that the lines represented by the following equations are coincident. | Pair Of Straight | SciPiPupil

Question: Prove that the lines represented by the following equation is coincident: $2x² +12xy +18y² = 0$.

Solution:

Given,

Equation of line is $2x² +12xy +18y² = 0$

$or, 2x² + 2×6xy + 18y² = 0$ - (i)

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

$a = 2, h = 6, and b = 18$

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

$or, h² = ab$

$or, 6² = 2×18$

$or, 36 = 36$ which is true.

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

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