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JEE MainMathematicsStraight Lines

Let A(2k, k) , k > 0 , be a point in the xy -plane. The image of A in the line y = x is B , and the image of B in the origin is C . If D is a variable point on the circle x^2 + y^2 = 18 such that the maximum area of BCD is 18 10 square units, then the value of k is

Correct answer

6

Step-by-step solution

A = (2k, k) B = (k, 2k) (image of A in the line y = x ) C = (-k, -2k) (image of B in the origin) The length of the base BC is (k - (-k))^2 + (2k - (-2k))^2 = 4k^2 + 16k^2 = 2k 5 . The line BC passes through the origin and its equation is y = 2x , or 2x - y = 0 . D is a point on the circle x^2 + y^2 = 18 , which is centered at the origin with radius 18 = 3 2 . Since the line BC passes through the center of the circle, the maximum distance from any point D on the circle to the line BC is exactly the radius of the cir

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