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The line y=mx+1 touches the curves y=-x^...

The line `y=mx+1` touches the curves `y=-x^(4)+2x^(2)+x` at two points `P(x_(1),y_(1))` and `Q(x_(2),y_(2))`. The value of `x_(1)^(2)+x_(2)^(2)+y_(1)^(2)+y_(2)^(2)` is

A

`4`

B

`6`

C

`8`

D

`10`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` The solution of `-x^(4)+2x^(2)+x=mx+1` is `x_(1)`, `x_(1)` and `x_(2)`, `x_(2)`.
`implies x^(4)-2x^(2)+(m-1)x+1=(x-x_(1))^(2)(x-x_(2))^(2)`
By comparing, we get
`x_(1)=1`, `x_(2)=-1`, `m=1impliesP(1,2)` and `Q(-1,0)`
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