Ellipses are oval-shaped curves that often show up on the ACT® Math section. They're similar to circles but stretched either horizontally or vertically. Understanding ellipses can help you answer some of the more advanced geometry questions on the test.
Let's start with a quick comparison to circles. The equation of a circle is (x²) + (y²) = r². Ellipses are similar, but with a few key differences.
Horizontal Ellipses
The equation for a horizontal ellipse is:
+ = 1
In this equation, 'a' is always greater than 'b'. This makes the ellipse stretch horizontally.
Vertical Ellipses
For vertical ellipses, we swap the positions of 'a' and 'b':
+ = 1
Here, 'a' is still greater than 'b', but its position in the equation makes the ellipse stretch vertically.
The key to identifying which is which? Look at the denominator with the larger value (a²). If it's under x², the ellipse is horizontal. If it's under y², the ellipse is vertical.
How Ellipses Appear on the ACT® Math
Ellipse questions typically show up in the later parts of the ACT® Math section, usually in the 50-60 range of questions. These are generally considered more challenging problems.
The ACT® might ask you to:
- Identify the correct equation for an ellipse based on a graph.
- Determine whether an equation represents a horizontal or vertical ellipse.
- Find the center, vertices, or foci of an ellipse.
The test makers aren't usually trying to trick you with complex calculations. They're more interested in seeing if you understand the basic structure of ellipse equations and can apply that knowledge.
When you encounter an ellipse question, take a moment to identify whether it's horizontal or vertical. This can often be the key to solving the problem quickly and accurately.
For more strategies on tackling difficult ACT® Math questions like these, check out my guide on question difficulty.