x2+ y2 – 20x + 8y + 115 = 0 What is the center of this circle? What is the radius of this circle ?

Question

x2+ y2 – 20x + 8y + 115 = 0
What is the center of this circle?
What is the radius of this circle ?

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Alaia 3 weeks 2021-11-18T13:32:47+00:00 1 Answer 0 views 0

Answers ( )

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    2021-11-18T13:34:36+00:00

    Answer:

    (10, – 4 ), r = 1

    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 the radius

    Given

    x² + y² – 20x + 8y + 115 = 0

    Collect the x- terms and collect the y- terms and subtract 115 from both sides.

    x² – 20x + y² + 8y = – 115

    Complete the square on both the x and y terms

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

    x² + 2(- 10)x + 100 + y² + 2(4)y + 16 = – 115 + 100 + 16

    (x – 10)² + (y + 4)² = 1 ← in standard form

    with centre = (10, – 4 ) and radius = 1

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