How does the equation change if the center is NOT at the origin?

When either 'h' or 'k' is not zero, the ellipse will be transformed to a position on the graph such that the center is not the origin. Identify the centers of the following hyperbolas. Click or touch each blank line to check your answers.

x minus three squared over four
(*x* − 3)^{2}
4
−
y plus two squared over nine
(*y* + 2)^{2}
9
= 1

Center Interactive button. Assistance may be required. __________ (3,-2)

y minus two squared over nine
(*y* − 2)^{2}
9
−
x squared over four
*x*^{2}
4
= 1

Center Interactive button. Assistance may be required. __________ (0,2)

x minus two squared over four
(*x* − 2)^{2}
4
−
y squared over four
*y*^{2}
9
= 1

Center Interactive button. Assistance may be required. __________ (2,0)

y minus two squared over nine
(*y* − 2)^{2}
9
−
x plus three squared over four
(*x* + 3)^{2}
4
= 1

Center Interactive button. Assistance may be required. __________ (-3,2)

Remember, the major and minor radii aren't affected by changes to *h* and *k*. For all hyperbolas above, the *horizontal* radius = 2 and* vertical *radius = 3. The direction the hyperbola opens (and the determination of 'a' and 'b') varies with whether the '*x*' term or the '*y*' term is the positive one.