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In the parabola given by x² - 2x + y - 2 = 0, let AB be a focal chord and S be the focus. If AS = l1, then what is the value of BS?
- l1
- 4l1/(4l1 - 1)
- l1/(4l1 - 1)
- 2l1/(4l1 - 1)
Correct answer: l1/(4l1 - 1)
Solution
(x-1)^2=-(y-3) has 4a=1 so a=1/4. For a focal chord 1/AS+1/BS=1/a=4, hence 1/BS=4-1/l1=(4l1-1)/l1, giving BS=l1/(4l1-1).
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