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 x2 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 y2 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.