Math

QuestionSolve the equation x2+y210y+21=0x^{2}+y^{2}-10y+21=0 for yy.

Studdy Solution

STEP 1

Assumptions1. The given equation is x+y10y+21=0x^{}+y^{}-10 y+21=0 . We are trying to rewrite the equation in the form of (x-h)^ + (y-k)^ = r^, which represents a circle with center at (h,k)(h, k) and radius rr.

STEP 2

First, we need to group the terms involving yy together.
x2+(y210y)+21=0x^{2} + (y^{2}-10y) +21 =0

STEP 3

We can rewrite the yy terms as a perfect square by adding and subtracting (10/2)2=25(10/2)^2 =25 inside the parentheses.
x2+[(y210y+25)25]+21=0x^{2} + [(y^{2}-10y +25) -25] +21 =0

STEP 4

This simplifies tox2+[(y)225]+21=0x^{2} + [(y-)^{2} -25] +21 =0

STEP 5

Now, we can rearrange the terms to get the equation in the form of (xh)2+(yk)2=r2(x-h)^2 + (y-k)^2 = r^2.
x2+(y5)2=2521x^{2} + (y-5)^{2} =25 -21

STEP 6

implify the right side of the equationx2+(y5)2=4x^{2} + (y-5)^{2} =4This is the equation of a circle with center at (0,5)(0,5) and radius 22.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord