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I need help in math can you please help me

I need help in math can you please help me-example-1

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We have to find the equation of a circunference with:


\begin{gathered} \text{Center}=(-3,7) \\ \text{Passes through the point P}=(-6,-2) \end{gathered}

As it is a circunference that passes through a point, we know that the distance between the center and the point must be the radius, as all points in a circunference are at the same distance from the center.

We will find then the radius, by calculating the distance:


\begin{gathered} d(C,P)=\sqrt[]{(-3-(-6))^2+(7-(-2)_{})^2} \\ =\sqrt[]{(-3+6)^2+(7+2)^2} \\ =\sqrt[]{3^2+9^2} \\ =\sqrt[]{9+81} \\ =\sqrt[]{90} \end{gathered}

Now, this means that the radius is √90.

We use the standard form for the equation of a circle:


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

where (h,k) is the center of the circle. In this case,


(h,k)=(-3,7)

And replacing, we obtain that the equation of the circle is:


\begin{gathered} (x+3)^2+(y-7)^2=(\sqrt[]{90})^2 \\ (x+3)^2+(y-7)^2=90 \end{gathered}

I need help in math can you please help me-example-1
User NutCracker
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