Consider a triangle whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of is (1, 1), then the equation of the circle passing through the vertices of the triangle is

JEE Advanced 2021 Mathematics question

Consider a triangle whose two sides lie on the -axis and the line . If the orthocenter of is , then the equation of the circle passing through the vertices of the triangle is

(A)
(B)Correct
(C)
(D)

Answer: (B)

Solution

The two given sides meet at . Let be the third vertex on the -axis and the third vertex on . The altitude from is perpendicular to the -axis and passes through , so it is and . The altitude from is perpendicular to (slope

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Question ID VK-033878