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Q.

Let P be a point on the parabola y2 = 4ax, where a > 0 . The normal to the parabola at P meets the x -axis at a point Q. The area of the triangle PFQ , where F is the focus of the parabola, is 120. If the slope m of the normal and a are both positive integers, then the pair  a,m is 

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a

(2,3)

b

(1,3)

c

(2,4)

d

(3,4)

answer is A.

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Detailed Solution

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Pat2,2at
Equation of normal is tx + y = 2at +at3
Q2a+at2,0 F(a,0) Pat2,2at
Area of  PFQ = 120
12a+at2(2at)=120 a1+t2(at)=120
Slope of normal = – t 
– t, a are integers 
a2t1+t2=120=(8)(15)=2(4)(3.5)=4(3)(10)m=t=3,a=2

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