# How do you write the equation for a circle touching y-axis and passing though the points (1,5), (8,12)?

##### 1 Answer

Aug 23, 2016

#### Explanation:

The general equation of a circle is

Where the centre is (a,b) and the radius is r

As the circle touches the y axis r=a

Draw any circle touching the y axis to see this.

So multiplying out gives:

This simplifies to

The point (1,5) is on the circle so substitute x =1 and y=5

Likewise (8,12) is on the circle.

You will have 2 simultaneous equation to find a and b.

Eliminate a to get to

So b=8 or 0

Think about b= 0

The centre of the circle is on the y axis and the circle touches the y axis!!!

So b=8 and you can calculate the value of a