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Find the radius of the circle \(2x^2 + 2y^2 - 4x + 5y + 1 = ...

Find the radius of the circle 2x2+2y24x+5y+1=0

A.

334

B.

56

C.

56

D.

334

Correct answer is A

Standard Form equation of a circle (Center-Radius Form): (xa)2+(yb)2=r2

Where "a" and "b" are the coordinates of the center and "r" is the radius of the circle

2x2+2y24x+5y+1=0

Divide through by 2

= x2+y22x+52y+12=0

=x22x+y2+52y=12

=x22x+12+y2+52y+(54)212516=12

=(x1)2+(y+54)2=12+1+2516

=(x1)2+(y(54))2=3316

=(x1)2+(y(54))2=(334)2

 r \frac{\sqrt33}{4} (answer)