A. 1 B. 7 54. What is the center and radius of the circle given by 8×2 + 8y2- 16x – 32y + 24 = 0? leng .T

Question

A. 1
B. 7
54. What is the center and radius of the circle given by
8×2 + 8y2- 16x – 32y + 24 = 0?
leng
.T
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Lyla 1 week 2021-09-12T13:36:17+00:00 1 Answer 0

Answers ( )

    0
    2021-09-12T13:37:37+00:00

    Step-by-step explanation:

    Given equation of circle (in general form) is:

    8 {x}^{2}  + 8 {y}^{2}  - 16x - 32y + 24 = 0 \\  \\ dividing \: throughout \: by \: 8 \: we \: find :  \\  {x}^{2}  + {y}^{2}  - 2x - 4y + 3 = 0  \\ equating \: it \: with :  \\  {x}^{2}  +  {y}^{2}  + 2gx + 2fy + c = 0 \\ 2g =  - 2 \implies \: g =  -  1\\  2f =  - 4 \implies \: f =  - 2 \\ c = 3 \\   \therefore \:center =  ( - g, \:  \:  - f) = (1, \:  \: 2) \\  \\ radius \: r =  \sqrt{ {g}^{2} +  {f}^{2}  - c }  \\  =  \sqrt{ {1}^{2}  +  {2}^{2}  - 3}  \\  =  \sqrt{1 + 4 - 3}  \\  =  \sqrt{5 - 3}  \\  =  \sqrt{2}  \: units

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