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

i am sure it will be 90 degrees.

step-by-step explanation:

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