Question

Write the equation of the circle centered at ( − 2 , 6 ) with radius 5

Answer 1

Step 1:

In this question, we are given the following:

Write the equation of the circle centered at ( − 2, 6 ) with a radius of 5.

Step 2:

The equation of a line is given as:

`\begin{gathered} \text{\lparen x - a\rparen}^2\text{ + \lparen y - b \rparen}^2\text{ = r}^2 \\ where\text{ \lparen a, b \rparen = \lparen - 2 , 6 \rparen} \\ \text{and r = 5} \end{gathered}`

This implies that:

`\begin{gathered} (\text{ x - \lparen- 2\rparen\rparen}^2\text{ + \lparen y - 6 \rparen}^2\text{ = 5}^2 \\ (\text{ x + 2 \rparen}^2\text{ + \lparen y - 6 \rparen}^2\text{ = 25} \end{gathered}`

The graph showing the equation of the circle is given as:

CONCLUSION:

The equation of the circle is given as:

`\text{\lparen x+ 2\rparen}^2\text{ + \lparen y-6 \rparen}^2\text{ = 25}`