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 $C (3, 5)$.
Given:
The point P $(–2, 4)$ lies on a circle of radius 6 and centre $C (3, 5)$.
To do:
We have to find whether the given statement is true or false.
Solution:
We know that,
The distance between the centre and a point on the circle is equal to the radius of the circle.
The distance between the point $P(-2,4)$ and centre $(3,5)=\sqrt{[3-(-2)])^{2}+(5-4)^{2}}$
$=\sqrt{(3+2)^{2}+(1)^2}$
$=\sqrt{5^2+1^2}$
$=\sqrt{25+1}$
$=\sqrt{26}$
The radius of the circle is 6.
Here,
The distance between the point $P(-2,4)$ and centre is not equal to the radius of the circle.
Therefore, the point P $(–2, 4)$ does not lie on the circle.
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