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Q. 36

Expert-verifiedFound in: Page 527

Book edition
Student Edition

Author(s)
Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages
227 pages

ISBN
9780395977279

** In Exercises 35-38 find an equation of the circle described and sketch the graph.**

** The circle has center (-2, -4) and passes through point (3, 8).**

The equation of the circle is${\left(x+2\right)}^{2}+{\left(y+4\right)}^{2}=169$

The graph is:

Given that the circle has center = (-2, -4) and passes through the point (3, 8).

We have to find the equation of the circle and sketch the graph.

We first find the length of the radius by finding the distance between (-2, -4) and (3, 8).

$\begin{array}{l}r=\sqrt{{\left(3-\left(-2\right)\right)}^{2}+{\left(8-\left(-4\right)\right)}^{2}}\\ r=\sqrt{{\left(3+2\right)}^{2}+{\left(8+4\right)}^{2}}\\ r=\sqrt{{\left(5\right)}^{2}+{\left(12\right)}^{2}}\\ r=\sqrt{25+144}\\ r=\sqrt{169}\\ r=13\end{array}$

Here, center = (*a, b*) = (-2, -4) and radius = *r* = 13.

We plug them in the standard form of the equation of a circle:

${\left(x-a\right)}^{2}+{\left(y-b\right)}^{2}={r}^{2}$

${\left(x+2\right)}^{2}+{\left(y+4\right)}^{2}={13}^{2}$

${\left(x+2\right)}^{2}+{\left(y+4\right)}^{2}=169$

So, the equation of the circle is ${\left(x+2\right)}^{2}+{\left(y+4\right)}^{2}=169$.

* *We will* *sketch the graph using a graphing utility.

Step 1: Press WINDOW button in order to access the Window editor.

Step 2: Press$\overline{)\text{Y=}}$ button.

Step 3: Enter the expression ${\left(x+2\right)}^{2}+{\left(y+4\right)}^{2}=169$ .

Step 4: Press GRAPH button to graph the function and then adjust the window.

The obtained graph is:

From the graph, we see that the center is (-2, -4) and the radius is 13.

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