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- anonymous

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- anonymous

The general form of the equation of a circle is Ax2 + By2 + Cx + Dy + E = 0, where A = B 0. If the circle has a radius of 3 units and the center at (0, 4), which set of values of A, B, C, D, and E correspond to the circle?
a)A = 0, B = 0, C = 2, D = 2, and E = 3
b)A = 1, B = 1, C = 8, D = 0, and E = 9
c)A = 1, B = 1, C = 0, D = -8, and E = 7
d)A = 1, B = 1, C = -8, D = 0, and E = 0
e)A = 1, B = 1, C = 8, D = 8, and E = 3

- welshfella

if we write the equation of a circle as
x^2 + y^2 + 2gx + 2fy + c = 0
then the center is (-g,-f)
and the radius is sqrt(g^2 + f^2 - c)
note there are no numbers before the x^2 and y^2 in the equation of a circle.

- welshfella

so for your circle you can see that A = 1 and B = 1

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- anonymous

sorry im horrible at math.
so do you substitute A and B for X and Y? and D and E for G and F?

- welshfella

if we write the 2 equations together we can compare
x^2 + y^2 + 2gx + 2fy + c = 0
Ax^2+ By^2 + Cx + Dy + e = 0
can you see that A and B = 1?

- welshfella

note x^2 is same as 1x^2

- anonymous

ok, so would the answer be B?

- welshfella

we dont know that yet we need to find C D and E
the center is at (0,4) meaning x = 0 and y = 4
if we compare this with (-g,-f) we see that -g = 0 so C =0
Follow?

- welshfella

and in the case of y = 4 , -f = 4 so f = -4 and 2f = -8
making D = 2f = -8

- anonymous

ok

- welshfella

now to work out e(which = c) we need to solve
radius r = sqrt(g^2 + f^2 - c)
3 = sqrt(0^2 + (-4)2 - e)

- welshfella

9 = 16 - e

- welshfella

so find e and you have your result

- anonymous

oh so its C. thank you for showing me how to do it

- welshfella

yw

- welshfella

yes e = 7 so its C

- welshfella

by writing the 2 equations together we can see that C - 2g , D = 2f and E = c

- welshfella

- that's called comparing coefficients

- anonymous

thank you =D

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