Question

The radius of a circle with centre at origin is 30 units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.

Answer 1

Radius of the circle = 30 units.

The point O is (0, 0).

Let a intersect the x-axis and b intersect the y-axis.

∴ The point A is (a, 0) and B is (0, b)

Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

OA = `sqrt(("a" - 0)^2 + (0 - 0)^2`

30 = `sqrt("a"^2)`

Squaring on both sides

30² = a²

∴ a = 30

The point A is (30, 0)

OB = `sqrt((0 - 0)^2 + ("b" - 0)^2`

= `sqrt(0^2 + "b"^2)`

30 = `sqrt("b"^2)`

Squaring on both sides

30² = b²

∴ b = 30

The point B is (0, 30)

Distance AB = `sqrt((30 - 0)^2 + (0 - 30)^2`

= `sqrt(30^2 + 30^2)`

= `sqrt(900 + 900)`

= `sqrt(1800)`

= `sqrt(2 xx 900)`

= `30sqrt(2)`

∴ Distance between the two points = `30sqrt(2)`