Question

The radius of a circle with centre (-2, 3) is 5
units. The point (2, 5) lies.
(a) on the circle (b) inside the circle
(c) outside the circle (d) None of these​

Answer 1

The point (2,5) lies inside the circle.

• To check whether a point lies inside or outside the circle, we write the equation of circle and substitute the point in the equation.
• If the value of the equation is equal to r² then the point lies on the circle.
• If the value of equation is less than r² then it lies inside the circle.
• And if the value of the equation is greater than r² then it lies outside the circle.
• Writing the equation of circle first,

$(x-h)^2+(x-k)^2 = r^2$, where (h,k) is the center of circle and r is the radius of the circle.

• Substituting the  values we get,

$(x-(-2))^2+(x-3)^2 = 5^2$

• Above equation is the equation of the circle.

• Now we have to find whether the point lies inside or outside the circle, we substitute the point in the equation of circle.

$(2-(-2))^2+(5-3)^2$

16+4 = 20 , which is less than r² = 5² =25.

• Therefore the point (2,5) lies inside the circle.