-the equation x^2 + y^2 -4x+2y=b how do you determine the y coordinate of the center of the circle. Also, if the radius of the circle is 7 units, what is the value of b in the equation?

1 Answer
Jim G.
Apr 29, 2018

#"centre "=(2,-1),b=44#

Explanation:

#"the standard form of the equation of a circle is"#

#color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))#

#"where "(a,b)" are the coordinates of the centre and r"#
#"is the radius"#

#"to obtain this form use "color(blue)"completing the square"#

#x^2-4x+y^2+2y=b#

#rArrx^2+2(-2)xcolor(red)(+4)+y^2+2(1)ycolor(magenta)(+1)=bcolor(red)(+4)color(magenta)(+1)#

#rArr(x-2)^2+(y+1)^2=b+5larrcolor(blue)"in standard form"#

#rArr"centre "=(2,-1)larr"y-coordinate "=-1#

#"if "r=7rArrr^2=49#

#rArrb+5=49rArrb=44#

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