Find+the+positive+value+for+α+if+th e+radius+of+the+circle+3x^2+3y-6αx+ 12y-3α=0+is+4

Step-by-step explanation:

Equation of a Circle

A circle of radius r and centered on the point (h,k) can be expressed by the equation

We are given the equation of a circle as

Note we have corrected it by adding the square to the y. Simplify by 3

Complete squares and rearrange:

We can see that, if r=4, then

Or, equivalently

There are two solutions for :

Keeping the positive solution, as required:

ratio is 2 : 9

the answer is three

13.5 : 3