Question

A focal chord to parabola y^2=16x is a tangent to circle (x-6)^2+y^2=2.then the slope is

Answer 1

Answer:

(1, -1 ) is the answer

Step-by-step explanation:

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Answer 2

Answer:

y^2=16x .....(i)

Here, 4a=16⇒a=4

Focus of the parabola (i) is (4,0)

Focal chord of the parabola is tangent to the circle (x−6)^2+y^2=2.

✓2and (6,0) are radius and centre of the circle

As radius is perpendicular to the tangent, we have length of tangent from (4,0) to the circle is =

✓2

.

From the diagram, we have

tan teta=✓2/✓2=1⇒θ=45

Therefore, slope of the chord is ±1=(−1,1).