Mathematics, 01.06.2021 09:30 200251

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).

3.a circle of radius 5 units passes through the points (- 3,3) and (3,1) .

i.how many circles can

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Answer from: darkcrystal463

See below

Step-by-step explanation:

Given:

Points (- 3,3) and (3,1) on a circler = 5

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:

C = ((-3 + 3)/2, (3 + 1)/2) = (0, 2)

The length of AB:

AB = $\sqrt{(3 + 3)^2 + (1 - 3)^2} = \sqrt{6^2+2^2} = \sqrt{40} = 2\sqrt{10}$

The distance AC = BC = 1/2AB = $\sqrt{10}$

The distance FC or GC is:

FC = GC = $\sqrt{5^2-10} = \sqrt{15}$

Possible coordinates of center are (h, k).

We have radius:

(h + 3)² + (k - 3)² = 25(h - 3)² + (k - 1)² = 25

Comparing the two we get:

(h + 3)² + (k - 3)² = (h - 3)² + (k - 1)²

Simplifying to get:

k = 3h + 2

We consider this in the distance FC or GC:

h² + (k - 2)² = 15h² + (3h + 2 - 2)² = 1510h² = 15h² = 1.5h = √1.5 orh = - √1.5

Then k is:

k = 3√1.5 + 2 ork = -3√1.5 + 2

So coordinates of centers:

(√1.5, 3√1.5 + 2) for G or(√1.5, 3√1.5 + 2) for F (or vice versa)

-------------------------------------------------------------------------------------

Diameters:

x - y - 4 = 02x + 3y + 7 = 0

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

x = 1, y = -3

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

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

r = $\sqrt{(2 - 1)^2+(4+3)^2} = \sqrt{1^2+7^2} = \sqrt{50}$

The equation of circle:

(x - 1)² + (y + 3)² = 50
3.a circle of radius 5 units passes through the points (- 3,3) and (3,1) .

i.how many circles can b

Answer from: Quest

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

Answer from: Quest

add an !

step-by-step explanation:

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3.a circle of radius 5 units passes through the points (- 3,3) and (3,1) . i. how many circles can...