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

Answers: 3

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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 correct answer here is c

Answer from: Quest

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

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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...

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