Write the radius of the circle x2 + y2 + 5x - 4y = 0.

square root (29)

square root (417/2)

square root (41)

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