How do you graph #x^2 + y^2 – 6x + 8y + 9 = 0#?

1 Answer
Alan P.
Apr 18, 2016

Draw a circle with radius #4# and center at #(3,-4)#

Explanation:

Given:
#color(white)("XXX")x^2+y^2-6x+8y+9=0#

Re-arrange into standard circle equation form:

Re-group:
#(x^2-6x)+(y^2+8y)=-9#

Complete the squares:
#(x^2-6xcolor(red)(+3^2))+(y^2+8ycolor(blue)(+4^2))=-9color(red)(+3^2)color(blue)(+4^2)#

Write as squared binomials and simplify the right side:
#(x-3)^2+(y+4)^2= 4^2#
or
#(x-color(green)(3))^2+(y-color(green)(color(white)("")(-4)))^2=color(brown)(4^2)#

Recalling that the standard circle equation is
#color(white)("XXX")(x-color(green)(a))^2+(y-color(green)(b))^2=color(brown(r)^2#
for a circle with center #(color(green)(a),color(green)(b))# and radius #color(brown)(r)#

The given equation is that of a circle with center #(color(green)(3),color(green)(color(white)("")(-4)))# and radius #color(brown)(4)#

graph{x^2+y^2-6x+8y+9=0 [-5.72, 12.066, -8.194, 0.69]}

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