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JEE Main20265 April 2026Evening ShiftMathematicsStraight LinesActual

From the point (-1, -1) , two rays are sent making angles of 45° with the line x + y = 0 . These rays get reflected from the mirror x + 2y = 1 . If the equations of the reflected rays are ax + by = 9 and cx + dy = 7 , a, b, c, d Z , then the value of ad + bc is _______.

Correct answer

0

Step-by-step solution

The given line is x + y = 0 , which has a slope of m₁ = -1 . Let the slope of an incident ray be m . Since it makes an angle of 45^ with the line x + y = 0 , we have: | m - (-1) 1 + m(-1) | = 45^ = 1 m + 1 1 - m = 1 Taking +1 : m + 1 = 1 - m 2m = 0 m = 0 Taking -1 : m + 1 = -1 + m 1 = -1 (which is not possible, implying m ). The incident rays pass through P(-1, -1) . Thus, their equations are: Ray 1: y = -1 Ray 2: x = -1 Next, we find the points of intersection of these incident rays with the mirror x + 2y = 1 . Fo

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