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Class 10 › Mathematics › Coordinate Geometry
CBSE2026Class Class 10 · Mathematics2 Marks · Short✅ Verified
A(-2, 3) and B(4, 1) are end points of the diameter of a semi-circle. The semi-circle intersects the y-axis at point P. Find the coordinates of the point P.
✅ Answer & Solution
Centre of circle = midpoint of AB $=\left(\frac{-2+4}{2},\frac{3+1}{2}\right)=(1,2)$.
Radius $=\frac12\sqrt{(4-(-2))^2+(1-3)^2}=\frac12\sqrt{36+4}=\sqrt{10}$
Circle equation: $(x-1)^2+(y-2)^2=10$. Putting $x=0$: $$1+(y-2)^2=10 \Rightarrow (y-2)^2=9 \Rightarrow y=5\text{ or }y=-1$$ Since P lies on the semicircle, the required point is **P(0, 5)**.
