Does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?​

Given equation of the Circle is ,

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

Hence the point lies within the circle .

inside the circle

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 25 ← is in this form

with r = = 5

Calculate the distance d from the centre to the point (- 4, 2 ) using the distance formula

d =

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 4, 2)

d=

   =

   =

    =

    ≈ 4.5 ( to 1 dec. place )

Since 4.5 is less than the radius of 5

Then (- 4, 2 ) lies inside the circle