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Pair of lines

Family of lin...

Question

Family of lines represented by the equation (costheta + sintheta)x + (costheta - sintheta)y - 3(3costheta + sintheta) =0 passes through a fixed point M for all real values of theta. The reflection of M in the line x-y=0 is
A)6,3
B)3,6
C)-6,3
D)3,-6

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Solution

dear student

$(\cos θ + \sin θ) x + (\cos θ - \sin θ) y - 3 (3 \cos θ + \sin θ) = 0 \cos θ (x + y - 9) + \sin θ (x - y - 3) = 0 (x + y - 9) + t a n θ (x - y - 3) = 0 L_{1} + k L_{2} = 0 p a s s e s t h r o u g h i n t e r s e c t i o n o f L_{1} a n d L_{2} f o r a l l v a l u e s o f k x + y - 9 = 0 x - y - 3 = 0 x + y = 9 x - y = 3 p o i n t o f i n t e r s e c t i o n i s (6, 3)$

regards

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