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.

Step-by-step 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