Write the standard form equation of the circle described.Centered at (−3,5)\left(-3,5\right); radius: 77

( x + 3 ) 2 + ( y − 5 ) 2 = 49 \left(x+3\right)^2+\left(y-5\right)^2=49

Write the standard form equation of the circle described. Centered at ( − 3 , 5 ) \left(-3,5\right) ; radius: 7 7

problem asks us to write the standard form equation of the circle described. Notice we have a circle where the center is at negative three five, and we have a radius of seven. Now, we should know that the standard form of a circle is x minus h squared plus y minus k squared is equal to r squared. Now you can see that my h and k are going to correspond to the center of our circle, And then I can see that my radius corresponds to the radius that we're given, or r. So because we have these, we can put our equation together. So we're going to have x minus negative three squared, and minus negative three is the same thing as plus three squared. We'll have plus y minus the k value, which is five squared, and all this is going to equal r squared, which is seven. Now seven squared is the same thing as 49, and this would be the equation of our circle given the information. Hope you found this video helpful.

Write the standard form equation of the circle described. Centered at ( − 3 , 5 ) \left(-3,5\right) ; radius: 7 7

( x + 3 ) 2 + ( y − 5 ) 2 = 49 \left(x+3\right)^2+\left(y-5\right)^2=49

( x − 3 ) 2 + ( y + 5 ) 2 = 49 \left(x-3\right)^2+\left(y+5\right)^2=49

( − 3 + x ) 2 + ( 5 + y ) 2 = 7 \left(-3+x\right)^2+\left(5+y\right)^2=7

( x + 3 ) + ( y − 5 ) = 7 \left(x+3\right)+\left(y-5\right)=7

14. Conic Sections & Systems of Nonlinear Equations

Graphing Circles

Beginning & Intermediate Algebra

14. Conic Sections & Systems of Nonlinear Equations

Graphing Circles

Struggling with Beginning & Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Write the standard form equation of the circle described.
Centered at $open paren negative 3 comma 5 close paren$ ; radius: $7$

${(x - 3)}^{2} + {(y + 5)}^{2} = 49$

${(- 3 + x)}^{2} + {(5 + y)}^{2} = 7$

${(x + 3)}^{2} + {(y - 5)}^{2} = 49$

$(x + 3) + (y - 5) = 7$

Verified step by step guidance

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

Identify the center coordinates from the problem: the center is at $(-3, 5)$, so $h = -3$ and $k = 5$.

Identify the radius from the problem: the radius is \$7$, so $r = 7$.

Substitute the values of $h$, $k$, and $r$ into the standard form equation: replace $h$ with $-3$, $k$ with \$5$, and $r^2$ with $7^2$.

Write the equation carefully, remembering that subtracting a negative number is the same as adding, so the equation becomes $\left(x - (-3)\right)^2 + \left(y - 5\right)^2 = 49$, which simplifies to $\left(x + 3\right)^2 + \left(y - 5\right)^2 = 49$.

4:32m

Watch next

Master Circles in Standard Form with a bite sized video explanation from Patrick Ford

Start learning