Question

12. 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

Answer:

The equation of the circle with centre at origin and radius 30 units will be

$x^2+y^2=30^2$

or, $\boxed{x^2+y^2=900}$

If we put y=0 in the above equation we get

$x=\pm 30$

And if we put x=0 in the equation of the circle we get

$y=\pm 30$

Therefore, the coordinates of the points where the circle intersects the axes are

$\boxed{(30, 0), (-30,0),(0,30) \text{ and }(0,-30)}$

The distance between two points on the x-axis or the y-axis will be equal to the diameter of the circle = 60 units

The distance between two points one lying on the x-axis and another on the y-axis will be

$=\sqrt{30^2+30^2}$

$=30\sqrt{2}$ units

Hope this helps.