SOLUTION: 3. A circle passes through A(-3,2) and has center O(1,5). (i) Find the radius of this circle. (ii) Use (i) to find the circle�s equation. (iii) Graph this circle. Expand your

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Question 907764: 3. A circle passes through A(-3,2) and has center O(1,5).
(i) Find the radius of this circle.
(ii) Use (i) to find the circle�s equation.
(iii) Graph this circle. Expand your scale wisely to make it clear on graph paper.
(iv) Label A and O with their coordinates.
(v) The circle passes through B(-2,b). Find b.
(vi) Add B to your graph and label it with its coordinates.
(vii) Draw the tangent line to the circle at B.
(viii) Find the equation of the line you just drew.
(ix) The line you just drew passes through the point E(100,c). Find c.
(x) Exactly how far is E from the center of the circle?

Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!
O(1,5)
A(-3,2) r = = 5
(x-1)^2 + (y-5)^2 = 5^2 circle�s equation
.........
O(1,5)
B(-2,9) r = = 5
........
B(-2,9)
O(1,5) m = 4/-3 = -4/3
m(tangent line) = 3/4
y-9 = (3/4)(x+2)
y = .75x +21/2 (tangent line)
.......
B(-2,9)
E(100,c) m = 4(9-c) = -306 c = 270/4 = 67.5 E(100,67.5)