SOLUTION: There are two concentric circles, whose areas are in the ratio 0.25. Determine the center if a straight line drawn from the center intersects the smaller and bigger circles at (2,

Question 897347: There are two concentric circles, whose areas are in the ratio 0.25. Determine the center if a straight line drawn from the center intersects the smaller and bigger circles at (2, 3) and (4, 8) respectively.
My answer is (0, -2). Am I correct? Please show me the working.
Answer by reviewermath(1029) (Show Source): You can put this solution on YOUR website!
Q:
There are two concentric circles, whose areas are in the ratio 0.25. Determine the center if a straight line drawn from the center intersects the smaller and bigger circles at (2, 3) and (4, 8) respectively.
My answer is (0, -2). Am I correct? Please show me the working.
A:
If (h,k) is the center of the circle, then the radius of the smaller circle is equal to and the radius of the bigger circle is . The ratio of the area of the smaller circle to the area of the bigger circle is equal to
= 0.25
= 0.25
Multiply both sides by 4 and expand.
=

The equation of the straight line is y = 2.5x - 2 so k = 2.5h - 2

Multiply both sides by 4.

Divide both sides by 29

h(3h - 8) = 0
h = 0 or h = 8/3
Using the equation k = 2.5h - 2.
If h = 0, then k = -2.
If h = 8/3, then k = 14/3.
There are two possible answers.
They are (0, -2) or (8/3, 14/3).

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