Parabola 2 Question 2

2. The tangents to the curve y=(x2)21 at its points of intersection with the line xy=3, intersect at the point

(a) 52,1

(b) 52,1

(c) 52,1

(d) 52,1

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Answer:

Correct Answer: 2. (c)

Solution:

  1. Given equation of parabola is

y=(x2)21y=x24x+3

Now, let (x1,y1) be the point of intersection of tangents of parabola (i) and line xy=3, then

Equation of chord of contact of point (x1,y1) w.r.t. parabola (i) is

T=0

12(y+y1)=xx12(x+x1)+3

y+y1=2x(x12)4x1+6

2x(x12)y=4x1+y16, this equation represent the line xy=3 only, so on comparing, we get

2(x12)1=11=4x1+y163x1=52 and y1=1

So, the required point is 52,1.



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