Question

26) Write the equation of the circle with center (0, 0) and (3, 6) a point on the circle. A) x2 + y2 = 9 B) x2 + y2 = 30 C) x2 + y2 = 45 D) x2 + y2 = 81

Answer 1

Answer:

C

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( where r is the radius )

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 ) = (0, 0) and (x₂, y₂ ) = (3, 6)

r = $\sqrt{(3-0)^2+(6-0)^2}$

  = $\sqrt{3^2+6^2}$

  = $\sqrt{9+36}$

  = $\sqrt{45}$ ⇒ r² = ($\sqrt{45}$ )² = 45, thus

x² + y² = 45 → C

Answer 2

Answer:C) x2 + y2 =45

Step-by-step explanation:

The equation of a circle in standard form is (x-h)2+(y-k)2=r2.

Since you know the center is (0,0), you can sub this is value in for h and k, then use the point (3,6) to sub in for x and y and you will find r2 =45. Hope that helps :)