Question

Write the equation in standard form for the circle passing through (6, 6) centered at the origin

Answer 1

Answer:

x² + y² = 72

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

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

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (6, 6)

r = $\sqrt{(6-0)^2+(6-0)^2}$

  = $\sqrt{6^2+6^2}$

  = $\sqrt{36+36}$

  = $\sqrt{72}$

Thus

x² + y² = ($\sqrt{72}$ )² , that is

x² + y² = 72 ← equation of circle