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:

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answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.