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Question

In the xy-plane, the parabola with equation y=(x11)2 intersects the line with equation y=25 at two points, A and B. What is the length of ¯¯¯¯¯¯¯¯AB?

A
10
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B
12
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C
14
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D
16
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Solution

The correct option is A 10
Given y=(x11)2
y=x222x+121
After substitute y=25. we get,
x222x+12125=0
x222x+96=0
(x16)(x6)=0
x=16,x=6
two points are A,B are (16,25),(6,25).
Distance between A and B is
(166)2(2525)2=10
Hence, option A is correct.

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