Question

HELP!!!!!! so many points for this one!!!!!! x^2+y^2+4x-2y=-1

The equation of a circle in the xy-plane is shown above. What is the radius of the circle

A.2
B.3
C.4
D.9

Answer 1

• A. 2

Explanation:

Given circle:

• x² + y² + 4x - 2y = -1

Convert the equation into the standard form of (x - k)² + (y - h)² = r²:

• x² + 4x + 4 + y² - 2y + 1 = -1 + 4 + 1
• (x + 2)² + (y - 1)² = 2²

As per above:

• r = 2

Correct choice is A

Answer 2

A.2

Answer:

Solution given:

equation of a circle is:

x²+y²+4x-2y=-1

x²+y²+4x-2y+1=0

Comparing above equation with

ax²+by²+2gx+2fy+c=0

we get

a=1

b=1

g=2

f=-1

c=1

now

radius of a circle (r)=
`√(g²+f²-c)`

substituting value

r=
`√(2²+(-1)²-1)=2`

therefore radius of a circle is 2 units