Select from the following two-variable quadratic equations those which are equations of circles. Determine the center and the radius of the circles.a. x2+y2+6x−4y+4=0b. x2+y2+2xy+5x−3y−5=0c. x2+y2−10x+6y+35=0d. −2x2−2y2+4x+8y+22=0

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junoon363km · Accepted Answer

The general equation of circle is x2+y2+2gx+2fy+c=0center is (−g,−f) and radius is 82+f2−ca) x2+y2+6x−4y+4=0Comparing this equation with the general equation we get:2g=6⇒g=32f=−4⇒f=−2R=32+(−2)2−4=3Therefore the center is (−3,2) and radius is 3.b) x2+y2+2xy+5x−3y−5=0This is not an equation of circlec) x2+y2−10x+6y+35=0This can be written as (x−h)2+(y−k)2=r2(x−5)2+(y+3)2=5.572Therefore the center is (5,−3) and radius is 5.57.d) −2x2−2y2+4x+y+22=0Divide the equation by -2x2+y2−2x−4y−11=0From comparing the above equation with the general equation we get:2g=−2⇒g=−12f=−4⇒f=−2R=12+22+11=1+4+11=4Therefore, center is (1,2) and radius is 4.

Select from the following two-variable quadratic equations those which are

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