Concept 8

Work with conic sections (parabolas/ellipses/hyperbolas) and their equations when presented.

Conic questions are mainly pattern-recognition: identify the curve and read its standard form.

Core Idea

Treat conics as pattern-recognition problems. One squared variable gives a parabola, two squared variables with the same sign give a circle or ellipse, and opposite signs give a hyperbola.

Understanding

Rule: ACT conic questions are usually about reading structure, not deriving formulas. After identifying the conic from its equation, use standard form to read the translated center, axis direction, or vertex information directly. For ellipses and hyperbolas, the larger denominator tells you which axis is longer or which direction the transverse axis runs.

A common trap is identifying the conic correctly but then reporting the semi-axis length when the question asked for the full axis length.

Question

Worked Example

For the ellipse (𝑥1)216 +(𝑦+2)29 =1, what is the length of the major axis?

Select an answer to see the explanation