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JEE Advanced 2016 Mathematics question

MathematicsStraight LinesJEE Advanced 2016

Let be the diameter of the circle , where is the point . Let be a variable point (other than and ) on the circle and tangents to the circle at and meet at the point . The normal to the circle at intersects a line drawn through parallel to at point . Then the locus of passes through the point(s)

Answer: (A),(C)

Solution

Let . Tangent at : ; tangent at : . They meet at . The line through parallel to is ; the normal at is . So

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Question ID VK-026532