Chapter 11: Q. 8 (page 773)

Find the center and radius of the circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$ . Graph the circle.

Short Answer

Expert verified

The center of the circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$ is, $(1, - 2)$ and the radius is, $4$ units.

The graph of the circle is,

Step by step solution

Step 1 Given equation is,

$x^{2} + y^{2} - 2 x + 4 y - 11 = 0$ .

The equation of the circle is, ${(x - h)}^{2} + {(y - k)}^{2} = a^{2}$

where $(h, k)$ is the center and $a$ is the radius.

Now simplify the given equation to the form of the circle.

$x^{2} + y^{2} - 2 x + 4 y - 11 = 0 x^{2} - 2 x + y^{2} + 4 y = 11 x^{2} - 2 x + {(1)}^{2} + y^{2} + 4 y + {(2)}^{2} = 11 + {(1)}^{2} + {(2)}^{2} {(x - 1)}^{2} + {(y + 2)}^{2} = 11 + 1 + 4 {(x - 1)}^{2} + {(y + 2)}^{2} = 16 {(x - 1)}^{2} + {(y + 2)}^{2} = {(4)}^{2}$

Step 2 Now compare the obtained equation with the equation of the circle.

We get, the center is, $(1, - 2)$ and the radius is, $4$ .

Now let us draw a graph for the given equation of the circle whose center is marked by the point $C$ .

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Find the center and radius of the circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$ . Graph the circle.

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 Now compare the obtained equation with the equation of the circle.

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Find the center and radius of the circlex2+y2-2x+4y-11=0. Graph the circle.

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 Now compare the obtained equation with the equation of the circle.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Find the center and radius of the circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$ . Graph the circle.