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Equations of Circles — Easy Worksheet 2
Grade 11 · Whoobee Name: ____________________ Date: __________
Use the standard form (x - h)² + (y - k)² = r².
How to solve
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Example
Find the center of the circle (x + 1)² + (y - 1)² = 25. Write it as (h, k).
Answer: (-1, 1)
Not quite. The answer is
💡 Compare with (x − h)2 + (y − k)2 = r2: (x − 4)2 gives h = 4. (y − 5)2 gives k = 5. The center is (4, 5).
✓ Correct!
Not quite. The answer is
💡 Compare with (x − h)2 + (y − k)2 = r2: (x − 4)2 gives h = 4. (y − 5)2 gives k = 5. The center is (4, 5).
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle (x - 3)² + (y - 3)² = 4. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The right side is r2 = 25, so r = √25 = 5.
✓ Correct!
Not quite. The answer is
💡 The right side is r2 = 25, so r = √25 = 5.
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle x² + (y - 2)² = 1. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Put h = -5, k = 1 and r = 5 into (x − h)2 + (y − k)2 = r2. Then x − (-5) = x + 5, y − 1 stays as it is, and r2 = 52 = 25. So the equation is (x + 5)2 + (y - 1)2 = 25.
✓ Correct!
Not quite. The answer is
💡 Put h = -5, k = 1 and r = 5 into (x − h)2 + (y − k)2 = r2. Then x − (-5) = x + 5, y − 1 stays as it is, and r2 = 52 = 25. So the equation is (x + 5)2 + (y - 1)2 = 25.
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle (x - 2)² + (y - 4)² = 16. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The marked center is (2, -3). The circle passes through (4, -3), 2 units to the right of the center, so r = 2. Put h = 2, k = -3 and r = 2 into (x − h)2 + (y − k)2 = r2. Then x − 2 stays as it is, y − (-3) = y + 3, and r2 = 22 = 4. So the equation is (x - 2)2 + (y + 3)2 = 4.
✓ Correct!
Not quite. The answer is
💡 The marked center is (2, -3). The circle passes through (4, -3), 2 units to the right of the center, so r = 2. Put h = 2, k = -3 and r = 2 into (x − h)2 + (y − k)2 = r2. Then x − 2 stays as it is, y − (-3) = y + 3, and r2 = 22 = 4. So the equation is (x - 2)2 + (y + 3)2 = 4.
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle (x - 2)² + (y + 4)² = 25. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Compare with (x − h)2 + (y − k)2 = r2: (x − 5)2 gives h = 5. (y − 3)2 gives k = 3. The center is (5, 3).
✓ Correct!
Not quite. The answer is
💡 Compare with (x − h)2 + (y − k)2 = r2: (x − 5)2 gives h = 5. (y − 3)2 gives k = 3. The center is (5, 3).
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle (x + 1)² + (y - 3)² = 9. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Put h = 0, k = 4 and r = 6 into (x − h)2 + (y − k)2 = r2. Then x − 0 = x, y − 4 stays as it is, and r2 = 62 = 36. So the equation is x2 + (y - 4)2 = 36.
✓ Correct!
Not quite. The answer is
💡 Put h = 0, k = 4 and r = 6 into (x − h)2 + (y − k)2 = r2. Then x − 0 = x, y − 4 stays as it is, and r2 = 62 = 36. So the equation is x2 + (y - 4)2 = 36.
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle (x + 2)² + (y - 5)² = 25. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The marked center is (0, -5). The circle passes through (2, -5), 2 units to the right of the center, so r = 2. Put h = 0, k = -5 and r = 2 into (x − h)2 + (y − k)2 = r2. Then x − 0 = x, y − (-5) = y + 5, and r2 = 22 = 4. So the equation is x2 + (y + 5)2 = 4.
✓ Correct!
Not quite. The answer is
💡 The marked center is (0, -5). The circle passes through (2, -5), 2 units to the right of the center, so r = 2. Put h = 0, k = -5 and r = 2 into (x − h)2 + (y − k)2 = r2. Then x − 0 = x, y − (-5) = y + 5, and r2 = 22 = 4. So the equation is x2 + (y + 5)2 = 4.
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle (x + 1)² + (y + 3)² = 1. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The right side is r2 = 36, so r = √36 = 6.
✓ Correct!
Not quite. The answer is
💡 The right side is r2 = 36, so r = √36 = 6.
💡 How to solve: Equations of Circles
A circle with center (h, k) and radius r has the equation (x - h)2 + (y - k)2 = r2. Watch the signs: (x + 3)2 means h = -3. If the equation is expanded, group the x-terms and the y-terms and complete the square for each one.
Try a similar one
Find the center of the circle (x - 5)² + (y - 5)² = 1. Write it as (h, k).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Equations of Circles — Easy Worksheet 2
Use the standard form (x - h)² + (y - k)² = r².