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Abhishek Pal 3 weeks, 2 days ago

21 degree and 159 degree

Yogita Ingle 5 months ago

The base equation for a circle centered at (h,k) with radius r is:

(x - h)2+ (y - k)2 = r2

If the points are concyclic, they all lie on the graph for the same circle.

Thus, all points are solutions to a single equation of the circle

WE can plug each point into the base equation, and obtain a system of equationd

FOR POINT (-2,10)

Equation 1:  (-2 - h)2 + (10 - k)2 = r2

FOR POINT (1,11)

Equation 2:  (1 - h)2+ (11 - k)2 = r2

FOR POINT (6,10)

Equation 3:  (6 - h)2 + (10 - k)2 = r2

FOR POINT (9,7)

Equation 4:  (9 - h)2 + (7 - k)2 = r2

From Equation 1 and 2 above, since they have 2 different expressions equivalent to r2, we can construct an equation involving variables x and h.

r2 = r2

(-2 - h)2 + (10 - k)2 = (1 - h)2 + (11 - k)2

(-2 - h)(-2 - h) + (10 - k)(10 - k) = (1 - h)(1 - h) + (11 - k)(11 - k)

(4 + 2h + 2h + h2) + (100 -10k - 10k + k2) = (1 - h - h + h2) + (121 - 11k - 11k + k2)

h2 + 4h + 4 + k2 - 20k + 100 = h2-2h + 1 + k2 -22k + 121

We can subtract h and k from both sides.

4h + 4 - 20k + 100 = -2h + 1 -22k + 122

4h -20k + 104 = -2h - 22k + 122

Move all h and k variables to the left ... move all constants to the right

6H + 2K = 18

SYSTEM EQUATION 1:   6h + 2k = 18

From equation 3 and 4 above, we go through the same process to obtain a second system equation.

r2 = r2

(6 - h)2 + (10 - k)2 = (9 - h)2 + (7 - k)2

(6 - h)(6 - h) + (10 - k)(10 - k) = (9 - h)(9 - h) + (7 - k)(7 - k)

36 - 6h - 6h + h2+ 100 - 10k - 10k + k2 = 81 - 9h - 9h + h2 + 49 = 7k - 7k + k2

h2 - 12h + 36 + k2 - 20k + 100 = h2 - 18h + 81 + k2- 14k + 49

Simplify, and subtract h2 and k2from both sides

-12h - 20k + 136 = -18h - 14k + 130

Move the h and k variables to the left, and the constants to the right

-12h + 18h - 20k + 14k = 130 - 136

6h - 6k = -6

SYSTEM EQUATION 1:  6h - 6k = -6

6h +2k = 18

6h - 6k = -6

Multiply the second equation by -1, we have ... -6h + 6k = 6

Adding the 2 equations, we have

6h + 2k = 18

-6h + 6k =  6

8k =24

k = 3

Using substitution of k=3 into equation 6h + 2k = 18,

6h + 2(3) = 18

6h + 6 = 18

6h = 12

h = 2

Now, use one of the points on the circle ... (1, 11) and (h,k) ... (2,3), to find the radius

(1 - 2)2 + (11 - 3)2 = r2

1 + 64 = r2

65 = r2

r = √65
Thus the equation of our circle is:
(x - 2)2 + (y - 3)2 = (√65)2

Maniha Sonkar 7 months, 3 weeks ago

Hindi

Anupam Shailesh 3 months, 3 weeks ago

20

Tarun Kumar 8 months, 2 weeks ago

5/(5-r)=26/6+r+1 5(5-r)=2*6*5/(6-r+1)(6-r)(5-r) (7-r)(6-r)=12 42-7r-6r-r2=12 -13r+r2+42-12=0 R2-13r+30=0 r2-3r-10r+30=0 r(r-3)-10(r-3)=0 =(r-3) (r-10) =r-3=0 , r-10=0 r=3, r=10 (r is greater than n)

Vinay Sen 9 months, 4 weeks ago

Social responsibility

Yogita Ingle 10 months, 3 weeks ago

Triangles are a three-sided polygon that consists of three edges and three vertices and the sum of internal angles of a triangle equal to 180o.

Sanket Wagh 9 months, 3 weeks ago

If (x-1, y+4)= (1 ,2) find the values of x and y ## myCBSEguide

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