A pair of perpendicular straight lines is drawn through the origin forming with the line: $2 x + 3 y = 6$ an isosceles triangle right angled at the origin.The equation to the pair of lines is

5 x^{2} - 24 x y - 5 y^{2} = 0

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5 x^{2} - 26 x y - 5 y = 0

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5 x^{2} + 24 x y - 5 y^{2} = 0

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

5 x^{2} + 26 x y - 5 y = 0

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Solution

The correct option is A $5 x^{2} - 24 x y - 5 y^{2} = 0$
The equation of the line
$2 x + 3 y = 6$
$2 x + 3 y - 6 = 0$
$a x + b y - h = 0$
$a = 2, b = 3, h = 0$
the equation of pair
$\frac{x^{2} - y^{2}}{4 h} = \frac{x y}{a + b}$
$\frac{x^{2} - y^{2}}{4 \times 6} = \frac{x y}{3 + 2}$
$\frac{x^{2} - y^{2}}{24} = \frac{x y}{5}$
$5 x^{2} - 5 y^{2} = 24 x y$
$5 x^{2} - 24 x y - 5 y^{2} = 0$

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