1. The equation of a circle is x^2 + y^2 + 6x – 4y + 4 = 0. What are the center and the radius of the circle? Show ALLLLLL your work

Question

1. The equation of a circle is x^2 + y^2 + 6x – 4y + 4 = 0. What are the center and the radius of the circle? Show ALLLLLL your work

in progress 0
Thu Giang 4 years 2021-07-16T23:11:15+00:00 1 Answers 20 views 0

Answers ( )

  1. vankhanh
    0
    2021-07-16T23:12:23+00:00
    Reply

    Answer:

    (2, -3) and r = 3.

    Step-by-step explanation:

    you can also plug this equation in desmos but I guess it’s good to know how to do it also:

    The equation of a circle is (x-h)^2 + (y-k)^2 = r^2

    Now in order to make a perfect square on both sides, we need to do this:

    First add 9 to both sides:

    x^2 + 6x + 9 + y^2 -4y +4 = 9.

    I purposely shifted it to show the perfect square created when you add 9 to both sides. Factor:

    (x+3)^2 + y^2 – 4y + 4 = 9.

    now the second bolded part is allso a perfect square. Factor:

    (x+3)^2 + (y-2)^2 = 9

    Based on the equation of a circle, the center must be at (2, -3) and the radius is the square root of 9 which is 3.

    🙂

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )