Question

Pls explain I have a test on this number 2

Answer 1

Hello there. To solve this question, we have to remember some properties about equations of circles.

Given the following equation:

`(x-x_0)^2+(y-y_0)^2=R^2`

It is called the equation of a circle with center at

`(x_0,\,y_0)`

And radius R.

In the question, it gives us two equations that we might describe the shape of the equation, considering its key features (center, foci, asymptotes, semi-major and semi-minor axes, if applicable).

We have that

`(x+4)^2+(y-2)^2=16`

Is the equation of a circle with center at (-4, 2) and radius equal to

`R=√(16)=4`

For the other equation

`(x-2)^2+(y-5)^2=64`

Is also the equation of a circle, with center at (2, 5) and radius equal to

`R=√(64)=8`