3.a circle of radius 5 units passes through the points (- 3,3) and (3,1) . i. how many circles can be drawn that meet the given criteria?
ii. what can be the centre of a circle(S)
b. the equation of any two diameters of a circle are given by the straight lines x-y-4=0 and 2x+ 3y + 7 =0.
find the equation of the circle if it passes through the point (2,4).​

Step-by-step explanation:

Given:

i.

There are possible two points that can have a distance of 5 units from both of the given points, so possible two centers, hence two possible circles.

ii.

Let the points are A and B and the centers of circles are F and G.

The midpoint of AB, the point C is:

The length of AB:

The distance AC = BC = 1/2AB =

The distance FC or GC is:

Possible coordinates of center are (h, k).

We have radius:

Comparing the two we get:

Simplifying to get:

We consider this in the distance FC or GC:

Then k is:

So coordinates of centers:

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b.

Diameters:

The intercession of the diameters is the center. We solve the system above and get. Not solving here as it is already a long

The point (2, 4) on he circle given.

Find the radius which is the distance between center and the given point:

The equation of circle:

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x