Q11. - Precalculus Enhanced with Graphing Utilities

Question

Write the general form of the circle with center $\left(4,-3\right)$ and radius 5.

Step-by-Step Solution

Answer

The general form of the equation is .

$x^2+y^2-8x+6y=0$

Step 1. Given information.

Consider the given information such that the center is $\left(4,-3\right)$ and radius is $5$.

Step 2. Standard form of circle x - h 2 + y - k 2 = r 2 is used to find general form where h , k is center and r is radius.

Using the standard form and substitute the values of $h,k$ and $r$.

$$\begin{gathered} {\left(x-4\right)}^2+{\left(y+3\right)}^2=5^2 \\ {x}^2+y^2-8x+6y+25=25 \\ {x}^2+y^2-8x+6y=0 \end{gathered}$$