Which of the following is an equation of a circle in the xy plane with center? 04 and a radius with endpoint? Four Thirds, five. All right, and we are given these following answer choices. Okay, so in order to answer this, you must remember what the equation of a circle looks like. So it looks like x minus h squared plus y minus k squared, that is equal to r squared, where the center of the circle is a h, k. So that is our center and the art is our radius.

Okay, so once you notice, then you can start really making the the equation and seeing which of the answers makes sense. So the center is 04. That means we're going to have have an equation that looks like x minus zero squared. So we're just going to be x squared plus y minus four, and all of that squared. Okay? And that is going to be equal to r squared.

So right away, we can eliminate what or we can eliminate. We can eliminate B and D because they have y plus four, but we want our answer to have y minus four. So we're down to a and c. Now, let's think about how we could incorporate the R. How do we find the radius? Well, the radius is just the distance from the center to the endpoint. And the way we do this is we use the distance formula, which is just the difference between the x values and a squared plus the difference between the y values. So our radius Can you let me write that here?

R squared is going To be equal to four over three minus zero squared plus five minus four squared, and that will equal 25 over nine. Well, that really leaves us with one answer choice and that is hey