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Centre–radius form
(x − h)² + (y − k)² = r²
Where: h = Centre–radius form, k = k, r = radius, x = x, y = y
Solved example
Given: k = 7, r = 5, x = 10, y = 4
Find: h (Centre–radius form)
- Formula: (-h + x)² + (-k + y)² = r²
- Rearranged for h: h = x - √((-k + r + y)·(k + r - y))
- Substitute the values: h = 10 - √((-4 + 5 + 7)·(4 + 5 - 7))
- Rearranged for h: h = x + √((-k + r + y)·(k + r - y))
- Substitute the values: h = 10 + √((-4 + 5 + 7)·(4 + 5 - 7))
- Result: h = 6 ; h = 14
Answer: h = 6
Calculator
How to calculate Centre–radius form
- Write down the formula: (x − h)² + (y − k)² = r².
- Note the known values (k, r, x, y).
- Substitute them and simplify to find h.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Centre–radius form?
The formula is (x − h)² + (y − k)² = r², where h = Centre–radius form, k = k, r = radius, x = x, y = y.
What is Centre–radius form when k = 7, r = 5, x = 10, y = 4?
h = 6. Substitute the values into (x − h)² + (y − k)² = r² and simplify.