Question

Write the equation of a circle with a center at (1,4) where a point on the circle is (4,8).

Answer 1

Answer:

(x - 1)² + (y - 4)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (1, 4), so

(x - 1)² + (y - 4)² = r²

The radius is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (4, 8)

r = $\sqrt{(4-1)^2+(8-4)^2}$

  = $\sqrt{3^2+4^2}$ = $\sqrt{9+16}$ = $\sqrt{25}$ = 5

Hence

(x - 1)² + (y - 4)² = 5², that is

(x - 1)² + (y - 4)² = 25 ← equation of circle