Joseph B. answered • 11/13/19
• Texas Certified and Experienced Teacher/Tutor
A rotated conic will have a Bxy term as well as the other terms mentioned above. To draw a rotated conic you calculate how much to tilt (Ø) the plane then calculate the formula for drawing the unrotated conic, without the Bxy term on the rotated plane then draw the conic on the rotated plane.
Formula for rotated conic: Ax2 + Bxy + Cy2+Dx + Ey + F = 0
Formula to find tilt for the rotated plane: cot (2Ø) = (A-C)/B. For Ø ∈ (-π/2, π/2).
Use Ø to find a formula without Bxy which, when drawn on the tilted plane, produces the same graph as the original equation on an un-tilted plane.
Make the following substitutions for x & y and when you simplify the expression Bxy will disappear:
x= x' cosØ - y' sinØ & y = x'sinØ + y'cosØ. (there are other methods to find the new equation as well)....
Once you substitute and simplify the equation will look like the following:
Ax'2+ Cy'2+Dx' + Ey' + F = 0
You will be able to draw the un-rotated conic on the tilted plane to produce the graph of the original equation on the un-tilted plane.
