Rotate the coordinates to remove the xy-term. Then, name the conic.
A) circle
B) hyperbola
C) ellipse
D) parabola

Question

Rotate the coordinates to remove the xy-term. Then, name the conic. 
A) circle 
B) hyperbola 
C) ellipse 
D) parabola

Quizplus · Accepted Answer

A conic with an xy-term cannot be a circle, as a circle has the form $(x-a)^2+(y-b)^2=r^2$ (no xy-term). It also cannot be an ellipse because the xy-term will stretch or tilt the shape, breaking the symmetry required for an ellipse. It cannot be a parabola because a parabola has either an x-term or a y-term but not both. Therefore, the only option left is a hyperbola. Rotating the coordinates will result in an equation of the form $\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$, which is the standard form of a hyperbola.

Rotate the Coordinates to Remove the Xy-Term