Chapter 11: Q. 11.13 (page 1077)

Write the standard form of the equation of the circle with center $(2, 1)$ that also contains the point $(- 2, - 2)$ .

Short Answer

Expert verified

The standard form of the equation of the circle is ${(x - 2)}^{2} + {(y - 1)}^{2} = 25$ .

Step by step solution

Step 1. Given information.

The center of the circle is $(2, 1)$ .

The circle also contains the point $(- 2, - 2)$ .

We have to write the standard form of the equation of this circle.

Step 2. Use the Distance Formula to find he radius

Distance formula is $\sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$ .

Substitute the values

localid="1645253431095" $(x_{1}, y_{1}) = (2, 1)) (x_{2}, y_{2}) = (- 2, - 2)$

Therefore, radius

r = \sqrt{{(- 2 - 2)}^{2} + {(- 2 - 1)}^{2}} = \sqrt{{(- 4)}^{2} + {(- 3)}^{2}} = \sqrt{16 + 9} = \sqrt{25} = 5

Step 3. Write the standard form of circle

Put $(h, k) = (2, 1) r = 5$ in the equation role="math" localid="1645253912371" ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ .

role="math" localid="1645253812528" ${(x - 2)}^{2} + {(y - 1)}^{2} = 5^{2} {(x - 2)}^{2} + {(y - 1)}^{2} = 25$

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Write the standard form of the equation of the circle with center $(2, 1)$ that also contains the point $(- 2, - 2)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use the Distance Formula to find he radius

Step 3. Write the standard form of circle

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Write the standard form of the equation of the circle with center (2,1) that also contains the point (−2,−2).

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use the Distance Formula to find he radius

Step 3. Write the standard form of circle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write the standard form of the equation of the circle with center $(2, 1)$ that also contains the point $(- 2, - 2)$ .