Question

A circle is centered at P(0,0). The point W(-6, √37) is on the circle. Where does the point Z(8,3) lie?

Answer 1

Answer:

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, $\sqrt{37}$)

r = $\sqrt{(-6-0)^2+(\sqrt{37-0)^2} }$

  = $\sqrt{36+37}$ = $\sqrt{73}$

Hence

x² + y² = ($\sqrt{73}$)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