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A $(-2, 3)$ and B $(4, 1)$ are end points of the diameter of a semi-circle.
The semi-circle intersects y-axis at point P. Find the co-ordinates of the point P.
The semi-circle intersects y-axis at point P. Find the co-ordinates of the point P.
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Solution:
Coordinates of centre O are $(\frac{-2+4}{2}, \frac{3+1}{2})$ i.e. $(1, 2)$ (
frac{1}{2})
Let the coordinates of point P be $(0, y)$ (1)
Now $OP^2 = OB^2 \Rightarrow 1^2 + (2 - y)^2 = 3^2 + 1^2$
$\Rightarrow y = 5$ or $y = -1$
Coordinates of P are $(0, 5)$ or $(0, -1)$. (
frac{1}{2})
Coordinates of centre O are $(\frac{-2+4}{2}, \frac{3+1}{2})$ i.e. $(1, 2)$ (
frac{1}{2})
Let the coordinates of point P be $(0, y)$ (1)
Now $OP^2 = OB^2 \Rightarrow 1^2 + (2 - y)^2 = 3^2 + 1^2$
$\Rightarrow y = 5$ or $y = -1$
Coordinates of P are $(0, 5)$ or $(0, -1)$. (
frac{1}{2})