Question

If sum of the slopes of the lines given by x² - 4pxy + 8y² = 0 is three times their product then p = ______.

Options

• `3/4`

• `1/4`

• 4

• 3

Answer 1

If sum of the slopes of the lines given by x² - 4pxy + 8y² = 0 is three times their product then p = `underline(3/4)`.

Explanation:

Given, pair of lines, x² - 4pxy + 8y² = 0

Which is in the form of ax² + 2hxy + by² = 0

According to question,

Sum of the slopes = 3 × product of the slopes

⇒ m₁ + m₂ = 3 × (m₁ m₂)

⇒ `(- (- 4"p"))/8 = 3 xx 1/8`

⇒ 4p = 3

⇒ p = `3/4`