Question

Write the equation in terms of a rotated x'y'-system using θ, the angle of rotation. Write the equation involving x' and y' in standard form. xy +16 = 0; θ = 45°.

A. X'^2/4 + y'^2/2= 1
B. y'^2=-32x'
C.y'^2/32+x'^2/32=1
D.y'^2/32-x'^2/32=1

Answer 1

definitely not c nor a which are ellipses. xy + 16 = 0 is a rectangular hyperbola. Rotation anticlockwise by 45 degrees yields a hyperbola of the form \[\frac{ x ^{2} }{ a ^{2} } - \frac{ y ^{2} }{ b ^{2} } = 1. \] looks like D is the only one that works although that would be a clockwise 45 degree turn.

Answer 2

Thank you so much