Question 735112: the extremities of the diameter of a circle have coordinates(-4,3)and (6,-2). then the length of the intercept which the circle makes on the y-axis is
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Step 1: Find the Midpoint (h,k) of AB:
h = A1 + B1
2
h = -4 + 6
2
h = 2
2
h = 1
k = A2 + B2
2
k = 3 + -2
2
k = 1
2
k = 0.5
From above, the center of our circle is (h, k) = (1, 0.5)
Calculate radius:
r = Square Root((y1 - x1)2 + (y2 - x2)2)
r = Square Root((6 - -4)2 + (-2 - 3)2)
r = ½Square Root((102 + -52))
r = ½√(100 + 25)
r = ½√125
r = ½√125
r = ½(11.1803398875)
r = 5.5902
Now calculate our circle equation using (h, k), and r
Find the equation of the circle with center (h,k) = (1,0.5) and radius r = 5.5902
The standard equation for a circle is (x - h)2 + (y - k)2 = r2
Plugging in our numbers, we get:
(x - 1)2 + (y - 0.5)2 = 5.5902^2
(x - 1)2 + (y - 0.5)2 = 31.25033604
plug x= 0
you will get two values of y
add up the two intercepts to get the length of the chord
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