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How do you find the center and radius of the circle $x^2 + y^2 – 2x -3 = 0$ ?

1 Answer

Sep 7, 2016

Center: $(1,0)$
Radius: $2$

Explanation:

Given
$color(white)("XXX")x^2+y^2-2x-3=0$

Converting into standard circle form:
$color(white)("XXX")(x^2-2x)+(y^2)=3$

$color(white)("XXX")(x^2-2x+1)+(y^2-0)=3+1$

$color(white)("XXX")(x-1)^2+(y-0)^2=2^2$

Which is the standard circle form with
$color(white)("XXX")$ center $(1,0)$ , and
$color(white)("XXX")$ radius $2$

Here's the graph of the original equation for verification:
enter image source here

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