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Suppose OABC is a reatangle in the xy-pl...

Suppose OABC is a reatangle in the xy-plane where O is the origin and A, B lie on the parabola `y=x^2`.Then C must lie on the curve

A

`y=x^(2)+2`

B

`y=2x^(2)+1`

C

`y=-x^(2)+2`

D

`y=-2x^(2)+1`

Text Solution

Verified by Experts

The correct Answer is:
A

`becauseOBbotOA`
`So,t_(1)t_(2)=-1`
`Now (h)/(2)=(t_(1)+t_(2))/(2)`
`t_(2)+t_(2)=h` . . . (1)
`also t_(1)^(2)+t_(2)^(2)=k`
`(t_(1)+t_(2))^(2)-2t_(1)t_(2)=k`
`h^(2)+2=k`
locus is `x^(2)+2=y`
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