px² -8xy +8y² = 0 | Find the value of p | Pair Of Straight Lines | SciPiPupil

Question: Find the value of p, if the lines represented by the following equations coincide to each other: $px² -8xy +8y² = 0$.

Solution:

Given,

Equation of line is $px² -8xy +8y² = 0$

$or, px² - 2×4xy + 8y² = 0$ - (i)

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

$a = p, h = 4, and b = 8$

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

$or, h² = ab$

$or, 4² = p×8$

$or, 16 = 8p$

$or, 8×2 = 8×p$

$\therefore p = 2$

Therefore, the required value of p, when the lines represented by the given equation coincide to each other is 2.

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