Trigonometric EquationHard

Question

A ray passing through (2, -3) is incident parallel to x-axis on a mirror lying along x2 - 4x + 8y + 12 = 0. Which of the following points lie on the reflected ray ?

Options

A.(6, -4)
B.(-2, -5)
C.(6, -1)
D.(2, 4)

Solution

       
Equation of mirror can be written as
(x - 2)2 = - 8(y + 1)
Vertex (2, -1), S : (2, -3), axis x =2
By reflection property incident ray is parallel tox - axis.
So, A(6, -3), B(-2, -3)
Hence equation of reflected ray can be
x = 6, x = -2

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