Chapter 1.4, Problem 14AYU

To determine

To write: The standard form and general form of the equation of the circle with radius 3 and centre $\left(\text{1, 0}\right)$

Answer to Problem 14AYU

$\text{The standard form of the equation of the circle is }\left(x\text{ - 1}\right)²\text{ + }y\text{² = 9, and general form of the equation of the circle is }x\text{² + }y\text{² - 2}x\text{ = 8}\text{.}$

Explanation of Solution

Given:

Radius $r\text{ = 3;}$ centre $\left(h,k\right)\text{ = }\left(\text{1, 0}\right)$

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 $r\text{ = 3}$ and $\left(h,k\right)=\left(\text{1, 0}\right)$ in the standard form of the equation.

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

$\left(x-1\right)²+\left(y-0\right)²=3\text{²}$

$\left(x-1\right)²+y²=9$

$x²-2x+1+y²=9$

$x²-2x+1+y²-1=9-1$   Subtract 1 from both sides

$x²+y²-2x =8$

General form of the equation of the circle is $x\text{² + }y\text{² <mo>−</mo> 2}x\text{ = 8}$.