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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.
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Solution
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)`
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