**IBDP** **Mathematics**** Question Analysis Topic: Mathematics - Circles**

**Exam Question:**

Find the equations of the circle touching both axes and passing through the point (2,1).

**Answer:**

For IBDP Mathematics, you should know:

Assume a circle with a radius of **r** and a center at the coordinates **(h,k)**.*Remember: the general equation of a circle is (x-h)*^{2}* + (y-k)*^{2}* = r*^{2}

^{With the given information, we can plot the above diagram.}

We can deduce that the radius of the circle is given by the above-drawn figure, which is **r=h=k**.

Therefore, the circle has a center of (**h,h**) and a radius of h.

Hence, the equation can be written as:

(x-h)^{2} + (y-h)^{2 }= h^{2 }*(i)* **=>** x^{2} + h^{2} - 2hx + y^{2} + h^{2} - 2hy = h^{2}

Simplified as:

x^{2} + y^{2} - 2hx - 2hy + h^{2} = 0 *(ii)*

Substituting** x = 2 and y = 1** in equation (ii), we will find that **h=5 and h=1**.

Hence, by substituting these two values into equation (i) (separately), we will come up with the two equations:

(x-5)^{2} + (y-5)^{2} = 25 and (x-1)^{2} + (y-1)^{2} = 1

Work hard for your IBDP Mathematics examination!

End of analysis. Great!