Find the equation of the bisectors of the angle between the lines represented by $3 x^{2} - 5 x y + 4 y^{2} = 0$

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

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

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

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$x^{2} - 2 x y - y^{2} = 0$

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Solution

The correct option is C
$5 x^{2} - 2 x y - 5 y^{2} = 0$

Given equation is

$3 x^{2} - 5 x y + 4 y^{2} = 0$

Comparing this equation of with standard pair of straight lines passing through origin $a x^{2} + 2 h x y + b y^{2} = 0$

We have a = 3, b = 4, $h = \frac{- 5}{2}$

Now the equation of the bisector of the angle between the pair of lines (1)

$\frac{x^{2} - y^{2}}{a - b} = \frac{x y}{h}$

Substituting the value of a,b and h

$\frac{x^{2} - y^{2}}{3 - 4} = \frac{x y}{\frac{- 5}{2}}$ ;

$\frac{x^{2} - y^{2}}{- 1} = \frac{2 x y}{- 5} o r 5 x^{2} - 5 y^{2} = 2 x y$

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

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Find the equation of the bisectors of the angle between the lines represented by 3x2−5xy+4y2=0

Find the equation of the bisectors of the angle between the lines represented by $3 x^{2} - 5 x y + 4 y^{2} = 0$