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Question

If the parabola x2=ay makes an intercept of length 40 units on the line y2x=1, then a is equal to

A
1
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B
2
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C
1
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D
2
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Solution

The correct option is B 2
Solving the equations x2=ay and y2x=1, we get
x2=a(2x+1)
x22axa=0
So, the given line cuts the parabola at two points (x1,y1) and (x2,y2)
x1+x2=2a and x1x2=a

Now, (40)2=(x1x2)2+(y1y2)240=(x1x2)2+(x21ax22a)240=(x1x2)2[1+(x1+x2)2a2]40=[(x1+x2)24x1x2](4a2a2+1)40=5(4a2+4a)a2+a2=0
(a+2)(a1)=0a=1,2

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