Acircle is centered at p(0,0). the point w(-6, √37) is on the circle. where does the point z(8,3) lie?

inside the circle, on the circle, outside the circle

On the circle

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.

To calculate r use the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

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

r =

  = =

Hence

x² + y² = ()²

x² + y² = 73 ← equation of circle

Substitute (8, 3) into the left side of the equation and

value < 73 → lies inside circle

value = 73 ← lies on the circle

value > 73 ← lies outside circle

(8, 3) → 8² + 3² = 64 + 9 = 73

(8, 3) lies on the circle

10000

step-by-step explanation: divide by 2,