Chapter 11: Q. 11.11 (page 1076)

Write the standard form of the equation of the circle with a radius of $7$ and center $(2, - 4)$ .

Short Answer

Expert verified

The equation of circle is ${(x - 2)}^{2} + {(y + 4)}^{2} = 49$ .

Step by step solution

Step 1. Given information.

The radius of the circle is $7$ .

The center of the circle is $(2, - 4)$ .

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

Step 2. Write the standard form of the equation of the circle

The standard form of the equation of a circle with radius $r$ and center $(h, k)$ is ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ .

Step 3. Substitute the values of radius and center

Put $(h, k) = (2, - 4)$

$r = 7$

The equation of the circle will be:

${(x - 2)}^{2} + {(y - (- 4))}^{2} = 7^{2} {(x - 2)}^{2} + {(y + 4)}^{2} = 49$

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Write the standard form of the equation of the circle with a radius of $7$ and center $(2, - 4)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the standard form of the equation of the circle

Step 3. Substitute the values of radius and center

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Write the standard form of the equation of the circle with a radius of 7 and center (2,−4).

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the standard form of the equation of the circle

Step 3. Substitute the values of radius and center

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Mechanics Maths

Discrete Mathematics

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Write the standard form of the equation of the circle with a radius of $7$ and center $(2, - 4)$ .