Get the answer to "Identify the center and ydius of each. 4x2−16x+y2−8y=1"

High School
Geometry
High school geometry
Circles

Nann

Answered question

2021-03-09

Identify the center and ydius of each. $4 x^{2} - 16 x + y^{2} - 8 y = 1$

Answer & Explanation

Nathalie Redfern

Skilled2021-03-10Added 99 answers

Write the equation in standard form of a circle with center (h,k) and radius r: ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$
Isolate the variable terms and group them: $x^{2} - 16 x + y^{2} - 8 y = 1$
$(x^{2} - 16 x) + (y^{2} - 8 y) = 1$
Complete the square:
$(x^{2} - 16 x + 64) + (y^{2} - 8 y + 16) = 1 + 64 + 16$
${(x - 8)}^{2} + (y - 4) 2 = 81$
or
${(x - 8)}^{2} + (y - 4) 2 = 9^{2}$
So, the center is (8,4) and radius is 9.

Jeffrey Jordon

Expert2021-08-12Added 2605 answers

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