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JEE MainMathematicsStraight Lines

Let A(3k, 4k) , k > 0 , be a point in the xy -plane. The image of A in the x -axis is B , and the image of B in the y -axis is C . If D is a variable point on the circle x^2 + y^2 = 25 in the second quadrant such that the maximum possible area of the quadrilateral ADCB is 146 square units, then the value of k is

Correct answer

2

Step-by-step solution

A = (3k, 4k) B = (3k, -4k) (image of A in the x -axis) C = (-3k, -4k) (image of B in the y -axis) The area of the quadrilateral ADCB can be split into the area of ABC and the area of ADC . For ABC , the base AB is vertical with length 8k . The perpendicular distance from C(-3k, -4k) to the line AB ( x = 3k ) is 6k . Area of ABC = 1 2 8k 6k = 24k^2 . For ADC , the base is AC . The length of AC is (-3k - 3k)^2 + (-4k - 4k)^2 = 10k . The line AC passes through the origin and its equation is 4x - 3y = 0 . Let D be (5 ,

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