Parabola 2 Question 32

11. The focal chord to y2=16x is tangent to (x6)2+y2=2, then the possible values of the slope of this chord are

(2003, 1M)

(a) 1,1

(b) 2,2

(c) 2,1/2

(d) 2,1/2

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Solution:

  1. Here, the focal chord of y2=16x is tangent to circle (x6)2+y2=2.

Focus of parabola as (a,0) i.e. (4,0)

Now, tangents are drawn from (4,0) to (x6)2+y2=2.

Since, PA is tangent to circle.

tanθ= slope of tangent =ACAP=22=1, or BCBP=1

Slope of focal chord as tangent to circle =±1



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