Chapter 1.4, Problem 20AYU

To determine

To write: The standard form and general form of the equation of the circle with radius $\frac{1}{2}$ and centre

Answer to Problem 20AYU

Explanation of Solution

Given:

Radius $r=\frac{1}{2}$; centre

Formula used:

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

$\left(x\text{ <mo><mo>−</mo></mo> }h\right)\text{² + }\left(y\text{ <mo><mo>−</mo></mo> }k\right)\text{² = }r\text{²}$

Calculation:

Substitute and in the standard form of the equation.

$\left(x\text{ <mo><mo><mo>−</mo></mo></mo> }h\right)\text{² + }\left(y\text{ <mo><mo>−</mo></mo> }k\right)\text{² = }r\text{²}$

$x²+y²+y+\frac{1}{4}=\frac{1}{4}$

   Subtract $\frac{1}{4}$ from both sides

$x²+y²+y=0$

General form of the equation of the circle is $x²+y²+y=0$.