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Point Slope Form of a Straight Line

Equation of t...

Question

Equation of the pair of straight lines through origin and perpendicular to the pair of straight lines $5 x^{2} - 7 x y - 3 y^{2} = 0$ is

3 x^{2} - 7 x y - 5 y^{2} = 0

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3 x^{2} + 7 x y + 5 y^{2} = 0

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3 x^{2} - 7 x y + 5 y^{2} = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 x^{2} + 7 x y - 5 y^{2} = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is A $3 x^{2} - 7 x y - 5 y^{2} = 0$
Given pair
$5 x^{2} - 7 x y - 3 y^{2} = 0$
On comparing above eq with $a x^{2} + 2 h x y + b y^{2} = 0$ we get
$a = 5, h = \frac{- 7}{2}, b = - 3$

Equation of pair of lines perpendicular to $5 x^{2} - 7 x y - 3 y^{2} = 0$
$x^{2} - \frac{2 h}{b} x y + \frac{a}{b} y^{2} = 0$
$x^{2} - \frac{- 7}{- 3} x y + \frac{5}{- 3} y^{2} = 0$
$3 x^{2} - 7 x y - 5 y^{2} = 0$

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