Question

Need help with question 5? just the answer and work

Answer 1

Step 1:

In this question, we are asked to find the equation of the circle with the given characteristics in standard form:

Step 2:

We need to get the distance between the two points:

(11 , - 7 ) and ( 17 , 13 )

`\begin{gathered} d\text{ =}√((x_2-x_1)^2+(y_2-y_1)^2) \\ where\text{ \lparen x}_1,\text{ y}_1)\text{ = \lparen 11, - 7\rparen} \\ \text{and } \\ (x_2,\text{ y}_2)\text{ = \lparen 17, 13\rparen} \end{gathered}`
`\begin{gathered} d=\sqrt{(17-11)^2+\text{ \lparen13-\lparen-7\rparen\rparen}^2} \\ d\text{ = }\sqrt{6^2+\text{ \lparen13+7\rparen}^2} \\ d\text{ =}√(36+400) \\ d\text{ =}√(436) \\ Radius\text{ =}(√(436))/(2) \end{gathered}`

Next:

`\begin{gathered} Using\text{ the equation of a circle in standard form, we have that:} \\ (x-a)^2+\text{ \lparen y-b\rparen}^2\text{ = r}^2 \\ where\text{ \lparen a , b \rparen= \lparen}(11+17)/(2),\text{ }(-7+13)/(2))\text{ = \lparen}(28)/(2),\text{ }(6)/(2))\text{ = \lparen 14, 3\rparen} \\ r=(√(436))/(2) \\ and \\ r^2\text{ =\lparen}^(√(436))/(2))^2=(436)/(4)=\text{ 109} \end{gathered}`
`\begin{gathered} (x-14)^2+\text{ \lparen y - 3\rparen}^2=\text{ 109} \\ (Equation\text{ of the circle in standard form\rparen} \\ \end{gathered}`

The graph is as follows: