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SAT Math skill page

SAT Circle Equations Practice

Connect circle formulas with coordinate geometry so radius, center, and distance questions become easier to spot.

Practice circle equations in DolphinPractice questions
10-15 min practice time3 questions on pageGeometry and Trigonometry
Practice time10-15 min
Practice questions3 questions
Best forGeometry and Trigonometry

What this tests

What to know for this SAT skill

Dolphin practice questions

Practice your skill

Question 1 of 3Easy
A circle has radius 4. What is its diameter?
  1. 2
  2. 4
  3. 8
  4. 16
Show answer and solution
Correct answerC. 8

Solution walkthrough

  1. The diameter is twice the radius, so 2 x 4 = 8.
Question 2 of 3Medium
The equation of a circle is (x - 3)^2 + (y + 2)^2 = 25. What is the radius?
  1. 3
  2. 5
  3. 10
  4. 25
Show answer and solution
Correct answerB. 5

Solution walkthrough

  1. In center-radius form, = 25, so r = 5.
Question 3 of 3Hard
A circle has center (1, 2) and passes through (4, 6). What is the radius?
  1. 3
  2. 4
  3. 5
  4. 7
Show answer and solution
Correct answerC. 5

Solution walkthrough

  1. Use distance from the center to the point: sqrt((4 - 1)^2 + (6 - 2)^2) = sqrt(9 + 16) = 5.

Avoid these traps

Common mistakes on this skill

Confusing radius and diameter

Diameter is twice the radius. Many SAT answer choices test this swap.

Reading r squared as r

In (x - h)^2 + (y - k)^2 = r^2, the number on the right is r squared.

Missing sign changes in the center

The center of (x - 3)^2 + (y + 2)^2 is (3, -2), not (-3, 2).

Study plan

How to practice this skill in Dolphin

Dolphin Web gives you a personalized SAT study plan with lessons, unlimited Pip AI help, practice questions, full-length tests, and mistake review. The iPhone and Android apps are free. See plans.

  1. Memorize area, circumference, and center-radius form.
  2. Mark whether the problem asks for radius, diameter, area, or circumference.
  3. For coordinate problems, draw the center and point before using distance.
  4. Check if the final answer should be exact, decimal, or in terms of pi.
Practice circle equations in Dolphin

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FAQ

Questions about SAT Circle Equations Practice

Are circle equations on SAT Math?

Yes. Circle questions can ask about formulas, coordinate geometry, radius, diameter, or interpreting equation form.

What circle equation should I know?

Know (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

How do circle questions connect to distance?

A radius is the distance from the center to a point on the circle, so coordinate circle problems often use the distance formula.