Question

What type of the circle is represented by x2 + y2 + 2x - 4y + 1 = 0​

Answer 1

Answer:

x

2

+y

2

−2x+4y+1=0

x

2

−2x+y

2

+4y+1=0

x

2

−2x+1

2

−1

2

+y

2

+4y+2

2

−2

2

+1=0

(x−2)

2

−1+(y+2)

2

−4+1=0

(x−1)

2

+(y+2)

2

=4

Comparing above equation with the standard equation of circle (x−h)

2

+(y−k)

2

=r

2

, we get

h=1,k=−2

∴ Centre of circle (1,−2)

Answer 2

Answer:

∴ Centre of circle (1,−2)

Step-by-step explanation:

x^2+y^2−2x+4y+1=0

x^2−2x+y^2+4y+1=0

x^2−2x+1^2 −1^2 +y^2+4y+2^2−2^2+1=0

(x−2) 2 −1+(y+2) 2−4+1=0

(x−1)^2 +(y+2)^2=4

Comparing above equation with the standard equation of circle (x−h)

2+(y−k)^2=r^2 , we get

h=1,k=−2