z^2+ y^2 + 8x – 16y + 31 = 0 What is the center of this circle ? What is the radius of this circle ?

Question

z^2+ y^2 + 8x – 16y + 31 = 0
What is the center of this circle ?
What is the radius of this circle ?

in progress 0
Delilah 4 weeks 2021-11-10T14:17:53+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-11-10T14:19:38+00:00

    Answer:

    (- 4, – 8 ), radius = 7

    Step-by-step explanation:

    The equation of a circle in standard form is

    (x – h)² + (y – k)² = r²

    where (h, k) are the coordinates of the centre and r is the radius

    Given

    x² + y² + 8x – 16y + 31 = 0

    Collect the x- terms, collect the y- terms together and subtract 31 from both sides.

    x² + 8x + y² – 16y = – 31

    Use the method of completing the square on the x and y terms

    add ( half the coefficient of the x/ y term )² to both sides

    x² + 2(4)x + 16 + y² + 2(- 8)y + 64 = – 31 + 16 + 64

    (x + 4)² + (y – 8)² = 49 ← in standard form

    with centre = (- 4, 8 ) and r = \sqrt{49} = 7

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )