# 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 $C (3, 5)$.

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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.

Updated on 10-Oct-2022 13:28:28