Question

If the center of a circle is (1, 1), and it has a radius of 5, which is another point on the circle?

Answer 1

Explanation:

The equation of this circle is:

(x - 1)² + (y - 1)² = 5²

Just supposing we choose x = 2. What's the corresponding y-value?

Actually, there are two unique y-values for each x value.

Let x = 2 in (x - 1)² + (y - 1)² = 5². Then:

(2 - 1)² + (y - 1)² = 5², or

1² + (y - 1)² = 25

Solving for (y - 1)², we get (y - 1)² = 25 - 4, or 24.

Taking the square root of both sides:

y - 1 = ±√24, so that y = 1 ±√24,

This simplifies to y = 1 ± 2√6.

Therefore, if x = 2, y has two values:

(2, 1+2√6) and

(2, 1-2√6