Question
State whether the following statements are true or false. Justify your answer.
The point P(-2, 4) lies on a circle of radius 6 and centre C(3, 5).
The point P(-2, 4) lies on a circle of radius 6 and centre C(3, 5).
✓
Answer
False:
The point P(-2, 4) lies on a circle if distance between P and centre is equal to the radius so distance of P from centre O(3, 5) will be
$\Rightarrow OP^2 = (-2 - 3)^2+ (-4 - 5)^2$
$\Rightarrow OP^2 = 25 + (-1)$
$\Rightarrow\text{OP}=\sqrt{26}\neq\text{radius }6$
So, P does not lie on the circle. It will lie inside the circle.
The point P(-2, 4) lies on a circle if distance between P and centre is equal to the radius so distance of P from centre O(3, 5) will be
$\Rightarrow OP^2 = (-2 - 3)^2+ (-4 - 5)^2$
$\Rightarrow OP^2 = 25 + (-1)$
$\Rightarrow\text{OP}=\sqrt{26}\neq\text{radius }6$
So, P does not lie on the circle. It will lie inside the circle.
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