Question

the x and y axis are tangent to a circle with radius 3 units. write a standard equation of the circle.

Answer 1

Given:

The x and y axis are tangent to a circle with radius 3 units.

To find:

The standard form of the circle.

Solution:

It is given that the radius of the circle is 3 units and x and y axis are tangent to the circle.

We know that the radius of the circle are perpendicular to the tangent at the point of tangency.

It means center of the circle is 3 units from the y-axis and 3 units from the x-axis. So, the center of the circle is (3,3).

The standard form of a circle is:

$(x-h)^2+(y-k)^2=r^2$

Where, (h,k) is the center of the circle and r is the radius of the circle.

Putting $h=3,k=3,r=3$, we get

$(x-3)^2+(y-3)^2=3^2$

$(x-3)^2+(y-3)^2=9$

Therefore, the standard form of the given circle is $(x-3)^2+(y-3)^2=9$.