Let A=(-1,2) and B=(1,-4). A circle is drawn with AB as diameter. If P(m,n) be a point on the circle,find the relation between m and n.?

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Answer 1 · 2018-02-23T08:37:59

See explanation.

From the given information we can calculate that:

The center of the circle is the midpoint of $A B$ $AB$ , so the center's coordinates are:

$S = (\frac{- 1 + 1}{2}; \frac{2 + (- 4)}{2}) = (0; - 1)$ $S=((-1+1)/2;(2+(-4))/2)=(0;-1)$

$r = | S A | = \sqrt{{(0 + 1)}^{2} + {(- 1 - 2)}^{2}} = \sqrt{10}$ $r=|SA|=sqrt((0+1)^2+(-1-2)^2)=sqrt(10)$

So the equation is:

$m^{2} + {(n + 1)}^{2} = 10$ $m^2+(n+1)^2=10$

If we move all terms to the left side we get: