Check the equation of the circle

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The discussion focuses on verifying the equations of circles based on given centers and points. The first equation proposed was (x-1)^2 + (y-1)^2 = 10, which was initially incorrect due to an error in identifying the center and radius. The correct equation for the first circle should reflect the center C(-1,2) and the radius derived from the distance to the x-intercept. The second equation, (x-4)^2 + (y+3)^2 = 20, was confirmed correct after clarifying that the center was provided, negating the need for a midpoint calculation. Ultimately, both equations were validated after corrections were made.
aisha
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check please the equation of the circle

the Center is C(-1,2) and the x intercept is 3

I found the distance between the center and the point to be r^2=10

and the midpoint of the two given points to be (1,1)

therefore my final equation for this circle is

(x-1)^2 + (y-1)^2 =10

is my answer correct? Any objections? :-p

Another question Equation of a circle with center (4,-3) that passes through the point (2,1)

for this question I got (x-4)^2 + (y+3)^2 =20

Is this one right?
 
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Unfortunately not quite. You don't need to find any midpoint at all: the center is given.

Also I don't like your radius. It should just be the distance between the two given points (which I calculate to be \sqrt{20}).
 
Your answer to the second question is correct.
 
oops ok I got my new answer to be

(x+1)^2 + (y-2)^2 = 20

is this correct now can you also check the second question in the first post? :redface:
 
Yep, they're both right now. :smile:
 

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