Let centre be $(h, k)$. Circle passes through origin: radius $= \sqrt{h^2 + k^2}$
Circle touches $x = 1$: radius $= |h - 1|$
$$h^2 + k^2 = (h-1)^2 \Rightarrow k^2 = -2h + 1$$
Locus: $y^2 = 2(x - 1)$ (parabola with vertex adjustment)
Back to JEE Main 2020 Coordinate Geometry
JEE Main 2020 — Mathematics Coordinate Geometry
medium
mcq
2020
Official previous-year question
Verified 30 May 2026.
Question
The locus of the centre of a circle which touches the line $x = 1$ and passes through the origin is:
Options
- A
$y^2 = 2(x-1)$
- B
$y^2 = 4(1-x)$
- C
$x^2 + y^2 = 1$
- D
$y^2 = 2x - 1$
Solution
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