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