Q. If $ax^{2} + by^{2} + 2gx + 2fy + c = 0$ represents an ellipse, then
A) It’s major axis is parallel to $x$-axis
B) It’s major axis is parallel to $y$-axis
C) It’s axes ($ie,$ major axis and minor axis) are neither parallel to $x$-axis nor parallel to $y$-axis
D) It’s axes are parallel to coordinates axes
Explanation
(d)
There is no $xy$ term so we can make perfect square in $x$ and $y$, from there it is clear that it’s axes are parallel to coordinates axes, but whether major axis is parallel to $x$ axis or parallel to $y$-axis depend on values of coefficients
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.