Question

Write the standard form of the equation of the circle described below.

Answer 1

Equation of circle is $x^2+(y+2)^2=26$

Step-by-step explanation:

The standard form of the equation of circle is:

$(x-h)^2+(y-k)^2=r^2$

where (h,k) is the center of the circle and r is the radius of circle.

We need to find the radius of circle r by using distance formula:

$r=d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\\r=d=\sqrt{(-5-0)^2+(-1-(-2))^2}\\r=d=\sqrt{(-5)^2+(1)^2}\\r=d=\sqrt{25+1}\\r=d=\sqrt{26}$

r=√26

and r^2= 26

Putting values of r^2=26 and value of center (h,k)=(0,-2)

the equation of Circle is:

$(x-h)^2+(y-k)^2=r^2\\(x-0)^2+(y-(-2)^2=26\\x^2+(y+2)^2=26$

Keywords: Equation of circle

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