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?

Inside the circle, on the circle, Outside the circle

Answer 1

On the Circle

Explanation:

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Answer 2

On the circle

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,
`√(37)`)

r =
`\sqrt{(-6-0)^2+(√(37-0)^2) }`

=
`√(36+37)` =
`√(73)`

Hence

x² + y² = (
`√(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