If the parabola `x^2=ay` makes an intercept of length `sqrt40` unit on the line `y-2x = 1` then `a` is equal to

Options

A. A. -1
B. B. -2
C. C. 1
D. D. 2

Answer

B, C

Explanation

2,3
Let line intersects parabola at `A(x_(1),y_(1))andB(x_(2),y_(2))`
Solving given parabola and line, we have
`x^(2)=a(1+2x)`
`:.x^(2)-2ax-a=0`
`So, x_(1)x_(2)=2aandx_(1)x_(2)=-a`
Now, `AB^(2)=(x_(1)-x_(2))+(y_(1)-y_(2))^(2)`
`=(x_(1)-x_(2))^(2)+((2x_(1)+1)-(2x_(2)+1))^(2)`
`=5(x_(1)-x_(2))^(2)`
`=5[(x_(1)+x_(2))^(2)-4x_(1)x_(2)]=5(4a^(2)+4a)`
`So,5(4a^(2)+4a)=40` (given)
`:." "a^(2)+a-2=0`
`:." "(a-1)(a+2)=0`
`:.a=-2,1`