Can you write the equation in standard form for the circle with center (0,3) passing through (0,9/2)?

Algebra 2

1 Answer
Apr 26, 2018

#x^2+(y-3)^2=9/4#

Explanation:

#"the equation of a circle in "color(blue)"standard form"# 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"#

#"here "(a,b)=(0,3)" but we require r"#

#"the radius is the distance from the centre to the given"#
#"point on the circumference "(0,9/2)#

#"since the x-coordinates of both points are zero then "#

#rArrr=9/2-3=9/2-6/2=3/2#

#"substituting into the equation gives"#

#(x-0)^2+(y-3)^2=(3/2)^2#

#rArrx^2+(y-3)^2=9/4larrcolor(red)"equation of circle"#