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# Tip #39 to Get a Top ACT Math Score

By Brian Leaf
McGraw-Hill Professional

I love this Skill. Yes, I do. And I'll tell you why. Almost every ACT has one question asking you to determine the equation of a circle. Nobody has this thing memorized, so the question is always ranked as a "medium," or even a "hard." But if you know the formula, it's totally easy! These are the best.

The formula for the equation of a circle is

(xh)2 + (yk)2 = r2

where (h, k) is the center of the circle and r is the radius. Memorize this and you will gain a point on your ACT score, guaranteed. Don't you love this book! In fact, I want you to take a study break right now to call two friends and recommend this book. Or, log onto Amazon.com and write a rave review expressing your gratitude and appreciation!

Let's look at this question:

Solution: The center is (4, 2), so h = 4 and k = 2. Plus, the radius is 5, so r = 5. Easy. Plug that into the equation for a circle, (xh)2 + (yk)2 = r2, which you have memorized. So the answer is E, or (x – 4)2 + (y – 2)2 = 25. Easy points!

### Medium

1. Which of the following best describes all points in a plane that are 5 inches from a given point in the plane?
1. A circle with a 5 inch radius
2. A circle with a 5 inch diameter
3. A circle with a 25 inch radius
4. A rectangle with 5 inch sides
5. A sphere with a 5 inch diameter
2. What is the center of the circle given by the equation (x – 8)2 + (y + 2)2 = 49 ?
1. (8, 2)
2. (7, 49)
3. (8, –2)
1. (7, –2)
2. (8, –7)
3. A circle in the standard (x, y) coordinate plane has center (5,–3) and radius 6 coordinate units. Which of the following is an equation of the circle?
1. (x – 5)2 – (y – 3)2 = 6
2. (x + 5)2 + (y + 3)2 = 6
3. (x – 5)2 + (y – 3)2 = 6
4. (x – 5)2 + (y + 3)2 = 36
5. (x + 5)2 – (y + 3)2 = 36
4. ### Hard

5. Which of the following is an equation of a circle with center at (1, 4) and tangent to the y axis in the standard (x, y) coordinate plane?
1. x2 + y2 = 1
2. x2y2 = 1
3. (x – 1)2 + (y – 4)2 = 2
1. (x – 1)2 + (y – 4)2 = 1
2. (x + 1)2 + (y + 4)2 = 1
6. A circle in the standard (x, y) coordinate plane is tangent to the x axis at 3 and tangent to the y axis at 3. Which of the following is an equation of the circle?
1. x2 + y2 = 3
2. (x – 3)2 – (y – 3)2 = 9
3. (x – 3)2 + (y – 3)2 = 3
4. (x – 3)2 + (y – 3)2 = 9
5. (x + 3)2 + (y + 3)2 = 9

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