A circle passes A(-4,-1) and B(2,1). How do you find the center and radius of this circle if the center of the circle is on y-axis?

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A circle passes A(-4,-1) and B(2,1). How do you find the center and radius of this circle if the center of the circle is on y-axis?

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Answer 1 · 2018-03-28T04:43:00

graph{x^2 +(y+3)^2=20 [-10, 10, -5, 5]}
Given that the center of the circle is on y-axis ( $x = 0$ $x=0$ ), let us consider the coordinates of its center $(O)$ $(O)$ be $(0, a)$ $(0,a)$

So

$O A^{2} = O B^{2} = R^{2}$ $OA^2=OB^2=R^2$ ,Where R is the radius of the circle.

$4^{2} + {(a + 1)}^{2} = 2^{2} + {(a - 1)}^{2} = R^{2}$ $4^2+(a+1)^2=2^2+(a-1)^2=R^2$

$\Rightarrow {(a + 1)}^{2} - {(a - 1)}^{2} = 2^{2} - 4^{2}$ $=>(a+1)^2-(a-1)^2=2^2-4^2$

$\Rightarrow 4 a = - 12$ $=>4a=-12$

$\Rightarrow a = - 3$ $=>a=-3$

Hence coordinates of the center (O) is (-3,0).

And radius $R = \sqrt{2^{2} + {(a - 1)}^{2}}$ $R=sqrt(2^2+(a-1)^2)$

$\Rightarrow R = \sqrt{2^{2} + {(- 3 - 1)}^{2}} = 2 \sqrt{5}$ $=>R=sqrt(2^2+(-3-1)^2)=2sqrt5$

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A circle passes A(-4,-1) and B(2,1). How do you find the center and radius of this circle if the center of the circle is on y-axis?

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