Answer:
r = √41
Step-by-step explanation:
recall that the general equation of a circle (in center-radius form) looks like
(x-h)² + (y-k)² = r²
where, r is the radius of the circle.
however we are given the general 2nd degree form:
x² + y² + 5x - 4y = 0
in order to convert this to the center radius form, we have to complete the square for x and y simultaneously:
x² + y² + 5x - 4y = 0 (rearrange)
x² + 5x + y² - 4y = 0 (group x and y terms)
(x² + 5x) + (y² - 4y) = 0 (complete the square)
[x² + 5x + (5/2)² ] + [y² - 4y + (-4/2)² ] = (5/2)²+ (-4/2)² (simplify)
[x+(5/2)]² + [y- (4/2)] ² = 25/4 + 4
[x+(5/2)]² + [y- 2] ² = 25/4 + 4
[x+(5/2)]² + [y- 2] ² = 41
[x+(5/2)]² + [y- 2] ² = (√41)²
if we compare this equation with the general equation above, we can clearly see that r = √41
