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in Mathematics by (53.3k points)

Let A and B be two distinct points on the parabola y2 = 4x. If the axis of the parabola touches a circle of radius r and AB is its diameter, then the slope of the line AB is

(a)   -1/r

(b)   1/r

(c)   2/r

(d)   -2/r

1 Answer

+1 vote
by (53.1k points)
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Best answer

Correct option   (C), (D)

Explanation :

Let A = (t12, 2t1) and B = (t22, 2t2)(t1 ≠ t2)Therefore, the slope of AB is

2/t1 + t2   ...(1)

Now, C is the centre of the circle described on AB as diameter  (see Fig), which is given by

Therefore, the radius is 

|t1 + t2| = r (∴ the circle touches the axis)

So, the slope of AB r = ± 2/r .

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