SOLUTION: I really need help with this, would appreciate any help. Show that the point E(-1 , 2) lies on the circumference of the circle with equation x2 + y2 – 2x – 3y – 1 = 0 and find

Algebra ->  Circles -> SOLUTION: I really need help with this, would appreciate any help. Show that the point E(-1 , 2) lies on the circumference of the circle with equation x2 + y2 – 2x – 3y – 1 = 0 and find      Log On


   

Question 986754: I really need help with this, would appreciate any help.
Show that the point E(-1 , 2) lies on the circumference of the circle with equation
x2 + y2 – 2x – 3y – 1 = 0 and find the coordinates of the point F,
given that EF is a diameter.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-2x%2By%5E2-3y-1=0
%28-1%29%5E2-2%28-1%29%2B%282%29%5E2-3%282%29-1=0
1%2B2%2B4-6-1=0
0=0
True, so point E satisfies the equation and therefore lies on the circle.
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Complete the square in x and y to find the center of the circle,x%5E2-2x%2By%5E2-3y-1=0
%28x%5E2-2x%2B1%29%2B%28y%5E2-3y%2B9%2F4%29-1=1%2B9%2F4
%28x-1%29%5E2%2B%28y-3%2F2%29%5E2=2%2B9%2F4
%28x-1%29%5E2%2B%28y-3%2F2%29%5E2=17%2F4
So the center of the circle is (1,3%2F2)
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The x distance from E to the center is the same as the x distance from the center to F.
d%5Bx%5D=1-%28-1%29=2
F%5Bx%5D=1%2B2=3
Similarly for y,
d%5By%5D=3%2F2-2=-1%2F2
F%5By%5D=3%2F2-1%2F2=1
So point F is (3,1)
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