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the end points of the diameter are at -4,-1 and 0,-4 anyone know how to find the equation of the circle or at least find the center and radius?

2007-09-02 14:36:25 · 6 answers · asked by Anonymous in Science & Mathematics Mathematics

6 answers

The center is the midpoint of the diameter; find the average of the endpoints. M = ( (-4+0)/2, (-1+-4)/2))

M = (-2, -2.5)

Radius is found using distance formula

r = sqrt [( 0 - -2)^2 + (-4 - -2.5)^2]

Equation: x + 2)^2 + (y + 2.5_^2 = r^2

2007-09-02 14:43:26 · answer #1 · answered by hayharbr 7 · 0 0

If A and B are the endpoints and P a point from the circle
AP and BP are perpendicular,so the product of their slopes=-1
so(
(y+1)/(x+4) * (y+4)/x +1=0

y^2+x^2+4x +5y+4=0

2007-09-02 21:48:34 · answer #2 · answered by santmann2002 7 · 0 0

yes use the horrible distance equation to find the length of the diameter.

half of the diameter will be the radius

delta x= -4 delta y = -3 half of that is
-2 -1.5

choosing one point and going half delta...

center should be at -2,-2.5 from symmetry

2007-09-02 21:56:50 · answer #3 · answered by 2hard4me 3 · 0 0

The centre is (-2,-2.5). The diameter's length is found using Pytagore's triangle equation so it's squareroot of 2.5 squared + 4 squared. Then your circonference is Pi(3.14159...) time the length of the diameter. The area is Pi time the square of the diameter divided by 2.
Check it out , it works.

2007-09-02 21:48:32 · answer #4 · answered by Khosro 1 · 0 0

The centre is just the mid-point of the line between the two points in the question. To find that, just average the x- and y- parts of the points.

The radius is just the distance between the centre (which you have just worked out) and either of the two given points (use Pythagoras).

Now you have the centre point (a.b) and the radius (c), the equation is just:
(x-a)^2 + (y-b)^2 = c^2

2007-09-02 21:44:58 · answer #5 · answered by SV 5 · 0 0

alternate method

eqn of the circle is

(x+4)(x-0) +(y+1)(y+4) =0

2007-09-02 22:48:08 · answer #6 · answered by qwert 5 · 0 0

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