Find the equation of the circle with diameter AB where A and B are the points (-1,2) and (3,3) respectively?

(x - 1)^{2} + (y - 2.6)^{2} = 4.26

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(x - 1)^{2} + (y - 2.5)^{2} = 4.25

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(x - 1)^{2} + (y - 2.3)^{2} = 4.29

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(x - 1)^{2} + (y - 2.8)^{2} = 4.24

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Solution

The correct option is B $(x - 1)^{2} + (y - 2.5)^{2} = 4.25$
$A B$ is diameter $⟹$ centre is midpoint of $A B$ which is $(\frac{- 1 + 3}{2}, \frac{2 + 3}{2}) = (1, 2.5)$
$A B = \sqrt{(- 1 - 3)^{2} + (2 - 3)^{2}} = \sqrt{17}$
$⟹$ radius $= \frac{A B}{2} = \frac{\sqrt{17}}{2}$
Equation of circle is $(x - 1)^{2} + (y - 2.5)^{2} = \frac{17}{4} = 4.25$

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Find the equation of the circle with diameter AB where A and B are the points (-1,2) and (3,3) respectively?

The correct option is B (x−1)2+(y−2.5)2=4.25AB is diameter ⟹ centre is midpoint of AB which is (−1+32,2+32)=(1,2.5)AB=√(−1−3)2+(2−3)2=√17⟹ radius =AB2=√172Equation of circle is (x−1)2+(y−2.5)2=174=4.25