The point P (–2, 4) lies on a circle of radius 6 and centre C (3, 5). Is the following statement true or false
Solution:
Given, the circle with radius 6 and centre C(3, 5)
We have to determine if the point P(-2, 4) lies on the circle.
We know that, if the distance of any point from the centre is
- less than the radius, then the point is inside the circle
- equal to the radius, then the point is on the circle.
- more than the radius, then the point is outside the circle.
The distance between two points P (x₁ , y₁) and Q (x₂ , y₂) is
√[(x₂ - x₁)² + (y₂ - y₁)²]
The distance between P(-2, 4) and C(3, 5)
PC = √[(3 - (-2))² + (5 - 4)²]
= √[(5)² + (1)²]
= √(25 + 1)
PC = √26
It is clear that PC < Radius of the circle
The distance between the point P from the centre is less than the radius of the circle.
Therefore, the point lies inside the circle.
✦ Try This: Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2, 3).
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7
NCERT Exemplar Class 10 Maths Exercise 7.2 Problem 11
The point P (–2, 4) lies on a circle of radius 6 and centre C (3, 5). Is the following statement true or false
Summary:
The statement “The point P (–2, 4) lies on a circle of radius 6 and centre C (3, 5)” is false. Since the distance between the point P from the center is less than the radius of the circle, the point P lies inside the circle
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