Question

find the center and radius of the circle with the given equationx²+y²-8x+10y=-16

Answer 1

Given:

$x^2+y^2-8x+10y=-16$

Required:

To find the center and radius of the given circle equation.

Explanation:

Consider the given equation,

$\begin{gathered} x^2+y^2-8x+10y=-16 \\ \\ x^2+y^2-8x+10y+16=0 \end{gathered}$

Now add and subtract 25 t the given equation ,

$x^2-8x+16+y^2+10y+25-25=0$$\begin{gathered} (x-4)^2+(y+5)^2-25=0 \\ \\ (x-4)^2+(y+5)^2=25 \\ \\ (x-4)^2+(y+5)^2=5^2 \end{gathered}$

Therefore,

The center is : (4,-5)

The radius is : 5

Final Answer:

The center is : (4,-5)

The radius is : 5