Q. 23 - Geometry

Question

Write an equation of the circle that has the given center and radius.

$C(-4,-7);r=5$.

Step-by-Step Solution

Answer

The equation of the circle is${\left(x+4\right)}^2+{\left(y+7\right)}^2=25$

Step-1 – Given

The given center = C(-4, -7) and radius = r = 5.

Step-2 – To determine

We have to find the equation of the circle.

Step-3 – Calculation

Given that center = (a, b) = (-4, -7) and radius = r = 5.

We will plug them in the standard form of a circle formula to get the equation:

${\left(x-a\right)}^2+{\left(y-b\right)}^2=r^2$

$\begin{array}{l}{\left(x-\left(-4\right)\right)}^2+{\left(y-\left(-7\right)\right)}^2={\left(5\right)}^2\\ {\left(x+4\right)}^2+{\left(y+7\right)}^2=25\end{array}$

So, the equation of the circle is ${\left(x+4\right)}^2+{\left(y+7\right)}^2=25$.