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Question

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

A
{1,1}
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B
{2,2}
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C
{2,12}
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D
{2,12}
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Solution

The correct option is A {1,1}
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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