Coordinate Geometry and Conics · Overview

Coordinate Geometry and Conics

Coordinate geometry questions put points, lines and curves in the standard (x, y) coordinate plane. Some ask for a distance, a midpoint or a slope; others ask for the equation of a parallel or perpendicular line, or for the center and radius of a circle hidden in an expanded equation.

Conic questions go further: the vertex and direction of a parabola, the axes of an ellipse, the vertices of a hyperbola, or which conic an equation describes. Some questions in this module move a point by a translation, a reflection or a rotation. ACT's test descriptions don't list a formula sheet, so know the common formulas; in this course, the ellipse and hyperbola standard forms are stated in the stem when a question depends on them.

How often it appears

Geometry makes up 17–20% of the Math section, about 8 or 9 of the 45 questions. This module covers the coordinate-plane part of that work: lines, circles, parabolas, ellipses, hyperbolas and moves on the grid.

You have 50 minutes for 45 questions, about 67 seconds each. Knowing the forms by heart, (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, y=a(x−h)2+ky = a(x - h)^2 + k and the rotation rules, keeps these questions well inside that time.

The question you’ll see

In the standard (x, y) coordinate plane, what are the center and radius of the circle with equation x2+y2−4x+6y=12x^2 + y^2 - 4x + 6y = 12?

In this module

  1. Overview Paid
  2. Distance, midpoint and slope Paid
  3. Parallel and perpendicular lines Paid
  4. Circle equations and completing the square Paid
  5. Parabolas: vertex form, axis and direction Paid
  6. Ellipses and hyperbolas: center and axes from the equation Paid
  7. Translations, reflections and rotations on the grid Paid
  8. Strategy summary Paid
  9. Mastery quiz Paid
  10. Pace check Paid