Fill in the blank(s) to correctly complete each sentence. The circle with equation x2+y2=$$49x^2$+y^2=49 $$has center with coordinates________ and radius equal to__________ .

Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

All textbooks

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 1

Chapter 3, Problem 1

Fill in the blank(s) to correctly complete each sentence. The circle with equation $x^{2} + y^{2} = 49$ has center with coordinates and radius equal to__ .

Verified step by step guidance

Recall the standard form of a circle's equation: $\left(x - h\right)^2 + \left(y - k\right)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius.

Compare the given equation $x^2 + y^2 = 49$ to the standard form. Notice that it can be rewritten as $(x - 0)^2 + (y - 0)^2 = 7^2$.

From this comparison, identify the center coordinates $(h, k)$ as $(0, 0)$ because there are no terms shifting $x$ or $y$.

Identify the radius $r$ by taking the square root of 49, which is $7$.

Therefore, the circle has center at $(0, 0)$ and radius equal to $7$.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Standard Form of a Circle Equation

The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center coordinates and r is the radius. Recognizing this form helps identify the center and radius directly from the equation.

Center of a Circle

The center of a circle is the point (h, k) from which all points on the circle are equidistant. In the equation x^2 + y^2 = 49, the center is at the origin (0, 0) because there are no (x - h) or (y - k) terms.

Radius of a Circle

The radius of a circle is the distance from the center to any point on the circle. It is found by taking the square root of the constant on the right side of the equation r^2. For x^2 + y^2 = 49, the radius is √49 = 7.

Recommended video:

5:18

Circles in Standard Form

Related Practice

Textbook Question

Without using paper and pencil, evaluate each expression given the following functions. $ƒ (x) = x + 1$ and $g (x) = x^{2}$

$open paren f with hook positive g close paren times 2$

views

Textbook Question

Fill in the blank to correctly complete each sentence. The point (4,_____ ) lies on the graph of the equation y = 3x - 6.

views

rank

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The graph of the line y= -2x+7 has slope ______ and y-intercept ______.

Textbook Question

Without using paper and pencil, evaluate each expression given the following functions. $ƒ (x) = x + 1$ and $g (x) = x^{2}$

$(ƒ - g) (2)$

views

Textbook Question

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. P(3, -1), Q(-4, 5)

views

Textbook Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x²? What is its domain?

views

Fill in the blank(s) to correctly complete each sentence. The circle with equation x2+y2=49x^2+y^2=49 has center with coordinates________ and radius equal to__________ .

Verified video answer for a similar problem:

Key Concepts

Standard Form of a Circle Equation

Center of a Circle

Radius of a Circle

Fill in the blank(s) to correctly complete each sentence. The circle with equation $x^{2} + y^{2} = 49$ has center with coordinates and radius equal to__ .