SOLUTION: Please help me find the x and y intercepts of this circle: 9x^2 + 9x^2 -6x +12y -31=0
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Question 314735: Please help me find the x and y intercepts of this circle: 9x^2 + 9x^2 -6x +12y -31=0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
is most emphatically not a circle. Can't be a circle without a y-squared term. However, I suspect you made a little typo and really meant:
Complete the square on x:
\ +\ 9y^2\ +\ 12y\ -\ 31\ =\ 1)
^2\ +\ 9y^2\ +\ 12y\ -\ 31\ =\ 1)
Complete the square on y:
^2+\ 9\left(y^2\ +\ \frac{4}{3}y\ +\ \frac{4}{9}\right)\ -\ 31\ =\ 1\ +\ 4)
^2+\ 9\left(y\ +\ \frac{2}{3}\right)^2\ -\ 31\ =\ 1\ +\ 4)
And put the rest of the constant in the RHS
^2+\ 9\left(y\ +\ \frac{2}{3}\right)^2\ =\ 36)
Multiply both sides by 
^2+\ \left(y\ +\ \frac{2}{3}\right)^2\ =\ 4)
Circle, center at )
and radius 2.
Substitute zero for 
^2+\ \left(y\ +\ \frac{2}{3}\right)^2\ =\ 4)
^2\ =\ \frac{35}{9})
\ =\ \pm\frac{\sqrt{35}}{3})
Hence, the intercepts are: )
and )
Just substitute 0 for y in the circle equation and do the arithmetic as above to find the 
-intercepts.
John
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