identify the conic sections below (circle,hyperbola,parabola,ellipse).

Question

a)3x2+3y2-2y=4
b)3x2-9y2+2x-4y=7
c)2x2+5y2-7x+3y-4=0
d)3y2-4x+17y=-10

Answer 1

hints:
1. Circles have equal coefficients of x² and y²
e.g. 2x²+2y²+3x-5y=17
2. hyperbola have different sign coefficients of x² and y²
e.g. 4x²-8y²-2x+5y=24
3. Parabolas have one of the squared terms missing,
e.g. x²-4x+4=0, or 2y²-4x+4=0
4. Ellipses have same sign coefficients of x² and y², but unequal numerically.
e.g. 2x²+4x+2y²-6y-46=0

(a) is an ellipse because both squared terms have a coefficient of 3.
(b)...(d) will be left as exercise for you.
Feel free to post your answers for checking. Please include justification.