Question

How do you write an equation for a circle with center (2,4) and passes through point (5, 9)?

Answer 1

The equation of a circle is:

(x - h)² + (y - k)² = radius²

where (h, k) is the center.

We can plug in the given information from the description and solve for the radius.

(x - 2)² + (y - 4)² = radius²

To find the radius, we do the distance formula from the center to the point on the circle.

Distance =
`\sqrt{ (Y2-Y1)^(2) + (X2 - X1)^(2) }`

D =
`\sqrt{ (9 - 4)^(2) + (5 - 2)^(2) }`
D =
`\sqrt{ 5^(2) + 3^(2) }`
D =
`√(25 + 9)`
D =
`√(34)`

That is your radius. Now we plug it in.

(x - 2)² + (y - 4)² = (√34)²

Your final answer is:

(x - 2)² + (y - 4)² = 34