Question

What is the area of a circle whose equation is (x-3)² + (y + 1) ² =81?

Answer 1

Okay, first, given the equation, we need to find out what the radius of the circle is. Let us state the general equation of a circle: 

$\frac{(x-x_{1})^2}{r^2}+ \frac{(y-y_{1})_^2}{r^2}=1$

Where $(x_{1}, y_{1})$ is the centre of the circle. In this case, we don't need to know the centre. Just the radius. 

Let us start by converting the equation into standard for, which I typed above. Divide both sides by 81. 

$\frac{(x-3)^2}{81}+ \frac{(y+1)^2}{81}=1$

Great! We now know the radius of the circle. It is $\sqrt{81}$ because it is the bottom fraction. Now we know that the radius is 9. 

So now lets input this into the area of circle formula: 

$A=πr^2$ 

Now we insert our radius. 

$A=9^2π$ 

$=A=81π$ 

You can convert that into a decimal if you wish. 

Hope this helped!

~Cam943, Moderator