OE

Equation of a circle, having origin as its centre, is in the form
𝑥^2 + 𝑦^2 = 𝑅^2

Where 𝑅 is the radius of the circle.
Given equation is 𝑥^2 + 𝑦^2 = 5^2

That is 𝑥^2 + 𝑦^2 = 25,
It’s a circle with a centre at origin and radius is equal to 5.

Let us check, for which all values of 𝑥 and 𝑦 in the first quadrant, the equation gets
satisfied.
We can observe, 𝑥 ranges from 0 to 5.
If 𝑥 = 0, then 𝑦 = 5.

If 𝑥 = 1, then 𝑦 = √24 , as √24 is not an integer so we will not consider this case
.so we cannot put 𝑥 as 1.
If we put 𝑥 = 2, then 𝑦 = √21 , as √21 is not an integer so we will not consider
this case also.
If we put 𝑥 = 3 then 𝑦 = 4,
As 𝑥 and 𝑦 both are integers so will consider this case.
So, we have (3,4) a point, which satisfy equation of circle as 3^2 + 4^2 = 25
If we put 𝑥 = 4 then 𝑦 = 3,
As 𝑥 and 𝑦 both are integers so will consider this case, also.
So, we have (4,3) a point, which satisfy equation of the circle as, 4^2 + 3^2 = 25
So, in the first quadrant we have two points which satisfy the equation of the circle.
Similarly, we’ll have two points in the second quadrant. As (- 3, 4) and (-4, 3).
We’ll have two points in the third quadrant. As (- 3, - 4) and (-4, -3)
And we’ll have two points in the fourth quadrant. As (3, -4) and (4, -3).
So, we have 8 points which satisfy the equation of line.
Now let us consider the points where the circle crosses 𝑥 and 𝑦 −axis.

Points (5,0), (0,5), (-5,0) and (0, -5) will satisfy the equation of line.
So, in total we have 12 points satisfying the equation of line.
Ans. (12)