Question 1
Classify the conic sections described by the following equations.
Then, compute their foci, directrix/directrices, and eccentricity:
1. x^2+9y^2=4.
Ellipse of the form: simplified further into or .
Center: (0,0)
Foci: so and the foci are
Eccentricity = c/a. So e= or
2. 4x^2−y^2=9.
Hyperbola of the form:
Center: (0,0)
Foci: and latus rectum at x = and x =
Eccentricity: e= which is
3. x^2+4xy+4y^2+6x+5y−1=0.
Slanted parabola of the form: