GATE 2025 CH – Question 9
A circle with center at $(x, y) = (0.5, 0)$ and radius = 0.5 intersects with another circle with center at $(x, y) = (1, 1)$ and radius = 1 at two points. One of the points of intersection $(x, y)$ is:
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Correct answer: (B) (0.2, 0.4)
Explanation
The circles are $x^2 - x + y^2 = 0$ and $x^2 + y^2 - 2x - 2y + 1 = 0$. Subtracting gives $x + 2y - 1 = 0$, so $x = 1 - 2y$. Putting this in the first circle: $(1 - 2y)^2 - (1 - 2y) + y^2 = 5y^2 - 2y = 0$, so $y = 0$ or $y = 0.4$. These give the points $(1, 0)$ and $(0.2, 0.4)$. Only $(0.2, 0.4)$ is among the options.