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Question: If the point P(4, –2) is the one end of the focal chord PQ of the parabola y<sup>2</sup> = x , then ...

If the point P(4, –2) is the one end of the focal chord PQ of the parabola y2 = x , then the slope of the tangent at Q is

A

–1/4

B

¼

C

4

D

–4

Answer

4

Explanation

Solution

The equation of the tangent at (4, –2) to y2 = x is –2y = 12\frac { 1 } { 2 } (x + 4) or x + 4y + 4 = 0.

Its slope is –14\frac { 1 } { 4 }.

Therefore the slope of the perpendicular line is 4. Since the tangents at the end of focal chord of a parabola are at right angle, the slope of the tangent at Q is 4.