Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A circle in the
xy-plane has the equation
x^(2)+y^(2)-14 y-51=0. What is the center of the circle?
Choose 1 answer:
(A)
(51,14)
(B)
(7,10)
(C)
(0,0)
(D)
(0,7)

A circle in the $x y$ -plane has the equation $x^{2}+y^{2}-14 y-51=0$ . What is the center of the circle? $\newline$ Choose $1$ answer: $\newline$ (A) $(51,14)$ $\newline$ (B) $(7,10)$ $\newline$ (C) $(0,0)$ $\newline$ (D) $(0,7)$

View step-by-step help

View step-by-step help

Find properties of circles from equations in general form

Full solution

Q. A circle in the

x y

-plane has the equation

x^{2}+y^{2}-14 y-51=0

. What is the center of the circle?

\newline

Choose

1

answer:

\newline

(A)

(51,14)

\newline

(B)

(7,10)

\newline

(C)

(0,0)

\newline

(D)

(0,7)

Complete the square for y terms: First, we need to complete the square for the y terms. $\newline$ $x^2 + y^2 - 14y = 51$ $\newline$ To complete the square, take half of the coefficient of y, square it, and add it to both sides. $\newline$ $(-14/2)^2 = 49$ $\newline$ $x^2 + y^2 - 14y + 49 = 51 + 49$
Rewrite with completed square: Now, rewrite the equation with the completed square. $x^2 + (y - 7)^2 = 100$
Identify center of circle: The equation $x^2 + (y - 7)^2 = 100$ is now in the form of a standard circle equation $(x - h)^2 + (y - k)^2 = r^2$ , where $(h, k)$ is the center of the circle. $\newline$ So, $h = 0$ and $k = 7$ .
Center corresponds to answer: The center of the circle is $(0, 7)$ , which corresponds to answer choice $(D)$ .

More problems from Find properties of circles from equations in general form

Question

Write the equation in standard form for the circle

x^2+y^2-9=0

\newline

Posted 3 months ago

Question

Write the equation in standard form for the circle with radius

2

centered at the origin.

\newline

Posted 3 months ago

Question

What is the center of the circle

x^2 + y^2 - 4 = 0

\newline

Simplify any fractions.

\newline

Posted 3 months ago

Question

What is the center of the circle

x^2 + y^2 = 144

?

\newline

Simplify any fractions.

\newline

\newline

Posted 3 months ago

Question

What is the radius of the circle

x^2 + y^2 = 36

\newline

Simplify any fractions.

\newline

Posted 3 months ago

Question

Write the equation in standard form for the circle with radius

11

centered at the origin. ______

Posted 3 months ago

Question

Write the equation in standard form for the circle

x^2+y^2+6x-1= 0

Posted 4 months ago

Question

Write the equation in standard form for the circle

x^2+y^2-4x+7= 0

Posted 4 months ago

Question

Write the equation in standard form for the circle

x^2+y^2-16= 0

Posted 4 months ago

Question

Write the equation in standard form for the circle

x^2+y^2+10y-25= 0

Posted 4 months ago