Published by:
CGP EDU Academic Team
Published on: August 13, 2026
A movable parabola touches the x and the y-axes at (1, 0) and (0, 1). Then the locus of the focus of the parabola is-
Text Solution
Verified by ExpertsThe correct answer is:
A
Since the x-axis and the y-axis are two perpendicular tangents to the parabola and both meet at the origin, the directix passes through the origin.
Let y = mx be the direction and (h, k) be the focus.
FA = AM
⇒ 
= 
… (1)
and FB = BN
= 
… (2)
From equation (1) and (2), we get
(h – 1) 2 + h 2 + k 2 + (k – 1) 2 = 1
⇒ 2x 2 – 2x + 2y 2 – 2y + 1 = 0 is the required locus.
Hence is correct answer.
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