How do you write the standard form of the equation of the circle with the given the center (7,-3); tangent to the x-axis?

1 Answer
Feb 2, 2016

Answer:

#(x-7)^2+(y-(-3))^2= 3^2# (explicit standard circle format)
or #(x-7)^2+(y+3)^2=9# (implicit standard circle format)
or #x^2+y^2-14x+6y+49# (standard polynomial format for an equation that happens to be a circle).

Explanation:

If the circle has a center at #(7,-3)# and is tangent to the X-axis
then it has a radius of #r=3#
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The explicit standard circle equation for a circle with center at #(x_c,y_c)# and radius #r# is
#color(white)("XXX")(x-x_c)^2+(x-y_c)^2=r^2#
which given the first version above #(x-7)^2+(y-(-3))^2=3^3#

Some (but not all) teachers like to see this expanded to get rid of the double minus signs and express the squared radius as a single entity:
#color(white)("XXX")(x-7)^2+(y+3)^3=9#

and still others are looking for the standard form of a general polynomial which is completely expanded with the right side as a series of terms in decreasing degree and the left side #=0#
(The third form above).