Select from the following two-variable quadratic equations those which are

cindakayumn 2022-03-03 Answered
Select from the following two-variable quadratic equations those which are equations of circles. Determine the center and the radius of the circles.
a. x2+y2+6x4y+4=0
b. x2+y2+2xy+5x3y5=0
c. x2+y210x+6y+35=0
d. 2x22y2+4x+8y+22=0
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Expert Answer

junoon363km
Answered 2022-03-04 Author has 8 answers
The general equation of circle is x2+y2+2gx+2fy+c=0
center is (g,f) and radius is 82+f2c
a) x2+y2+6x4y+4=0
Comparing this equation with the general equation we get:
2g=6g=3
2f=4f=2
R=32+(2)24=3
Therefore the center is (3,2) and radius is 3.
b) x2+y2+2xy+5x3y5=0
This is not an equation of circle
c) x2+y210x+6y+35=0
This can be written as (xh)2+(yk)2=r2
(x5)2+(y+3)2=5.572
Therefore the center is (5,3) and radius is 5.57.
d) 2x22y2+4x+y+22=0
Divide the equation by -2
x2+y22x4y11=0
From comparing the above equation with the general equation we get:
2g=2g=1
2f=4f=2
R=12+22+11=1+4+11=4
Therefore, center is (1,2) and radius is 4.
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