Question

Write the equation of a circle with center (4, -5) and radius = square root of 13

Answer 1

The required equation in standard form is
`(x-4)^2+(y+5)^2=13`

Explanation:

The equation of a circle with center (h,k) an radius, r units is given by the formula;

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

The given circle has center (4,-5) and radius
`r=√(13)`.

We substitute these values into the formula to obtain;

`(x-4)^2+(y--5)^2=(√(13))^2`

We simplify to get;

`(x-4)^2+(y+5)^2=13`

Answer 2

Hello!

The answer is:

The equation of the given circle is:

`(x-4)^(2)+(y+5)^(2)=13`

Why?

The equation of a circle is given by the following equation:

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

We are given the center point (4,-5) and the radius.

So,

Where:

`h=x=4\\k=y=-5\\r=√(13)`

Then, substituting into the circle equation, we have:

`(x-4)^(2) +(y-(-5))^(2)=(√(13))^(2)`

`(x-4)^(2) +(y-(-5))^(2)=(√(13))^(2)`

Hence, the simplified equation of the circle is:

`(x-4)^(2)+(y+5)^(2)=13`

Have a nice day!