Chapter 1.4, Problem 11AYU

To determine

To write: The standard form and general form of the equation of the circle with radius 2 and centre $\left(0,0\right)$

Answer to Problem 11AYU

$\text{The standard form and general form of the equation of the circle is }x\text{² + }y\text{² = 4}\text{.}$

Explanation of Solution

Given:

Radius $r\text{ = 2;}$ centre $\left(h,k\right)\text{ = }\left(\text{0, 0}\right)$

Formula used:

The standard form of an equation of a circle with radius $r$ and centre $(h,k)$ is:

$\left(x-h\right)\text{² + }\left(y-k\right)\text{² = }r²$

Calculation:-

Substitute $r\text{ = 2}$ and $\left(h,k\right)=\left(\text{0},\text{0}\right)$ in the standard form of the equation.

$\left(x-h\right)\text{² + }\left(y-k\right)\text{² = r²}$

$x²+y²=4$

General form of the equation of the circle is also $x²+y²=4$.