Answer: x 2 /a 2 + y 2 /b 2 = 1, a > b.
- A x<sup>2</sup>/a<sup>2</sup> + y<sup>2</sup>/b<sup>2</sup> = 1, a > b
- B x<sup>2</sup>/a<sup>2</sup> - y<sup>2</sup>/b<sup>2</sup> = 1
- C y<sup>2</sup> = 4ax
- D x<sup>2</sup> + y<sup>2</sup> = a<sup>2</sup>
Correct answer: A. x<sup>2</sup>/a<sup>2</sup> + y<sup>2</sup>/b<sup>2</sup> = 1, a > b
Explanation: x<sup>2</sup>/a<sup>2</sup> + y<sup>2</sup>/b<sup>2</sup> = 1 with a > b > 0 is the standard ellipse equation with the major axis along the x-axis.
All four conics form a single family distinguished only by eccentricity: a circle is the most "closed" (e=0), an ellipse is an elongated closed curve, a parabola is the borderline open curve (e=1), and a hyperbola has two separate open branches (e>1).
Concept context
Study circles, parabolas, ellipses, and hyperbolas as curves formed by intersecting a plane with a double cone, with their standard equations and key properties.