ABC is a triangle, where the vertices A and B are fixed points both lying on the x-axis. Let AB=10 cm. The vertex C moves such that 1 A + 1 B = 1 k , where k 0. What is the equation of the locus of the point C?

NDA 2026 Mathematics question

is a triangle, where the vertices and are fixed points both lying on the -axis. Let cm. The vertex moves such that , where . What is the equation of the locus of the point ?

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

Answer: (A)

Solution

Let and let be the foot of the perpendicular from to (the -axis), so . Then and (signed lengths, valid for acute or

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Question ID VK-030430