Pair of straight lines

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$If the pair of lines 6 x^{2} - α x y - 3 y^{2} - 24 x + 3 y + b = 0$ $intersect on x -axis, then α is equal to$

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Solution

$T h e p o i n t o f i n t e r s e c t i o n o f l i n e s r e p r e s e n t e d b y t h e c o m b i n e d e q u a t i o n a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0 i s (\frac{h f - b g}{a b - h^{2}}, \frac{g h - a f}{a b - h^{2}})$
$I f t h e l i n e s i n t e r s e c t o n x - a x i s t h e n i t s y - c o o r d i n a t e i s z e r o$
g=-12, h= $- α$ , a=6, f= $\frac{3}{2}$
$i t g i v e s g h - a f = 0 S u b s t i t u t e t h e a p p r o p r i a t e v a l u e s i n t h e a b o v e e q u a t i o n - \frac{α}{2} (- 12) - 6 (\frac{3}{2}) = 0$
$6 α - 9 = 0, α = \frac{3}{2}$

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Pair of straight lines

Remember concepts with our Masterclasses.

If the pair of lines 6x2−αxy−3y2−24x+3y+b=0 intersect on x -axis, then α is equal to

Ready to Test Your Skills?

free study material

$If the pair of lines 6 x^{2} - α x y - 3 y^{2} - 24 x + 3 y + b = 0$ $intersect on x -axis, then α is equal to$