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The vertex of the parabola whose paramet...

The vertex of the parabola whose parametric equation is `x=t^2-t+1,y=t^2+t+1; t in R ,` is

A

(1,1)

B

(2,2)

C

(1/2, 1/2)

D

(3,3)

Text Solution

Verified by Experts

The correct Answer is:
A
(1) `x=t^(2)-t+1,y=t^(2)+t+1`
`orx+y=2(t^(2)+1)andy-x=2t`
`or(x+y)/(2)=1+((y-x)/(2))^(2)`
`or(y-x)^(2)=2(x+y)-4`
`or(y-x)^(2)=2(x+y-2)`
Vertex will be the point where the lines where the lines y-x=0 and x+y-2=0 meet, i.e., the point (1,1).
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CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
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  10. The number of common chords of the parabolas x=y^2-6y+11 and y=x^2-6x+...

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  11. Two parabola have the same focus. If their directrices are the x-and t...

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  12. PSQ is a focal chord of a parabola whose focus is S and vertex is A. P...

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  13. If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , the...

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  14. The triangle P Q R of area A is inscribed in the parabola y^2=4a x suc...

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  15. If A1B1 and A2B2 are two focal chords of the parabola y^2=4a x , then ...

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  16. If a and c are the lengths of segments of any focal chord of the parab...

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  17. If y=m x+c touches the parabola y^2=4a(x+a), then (a)c=a/m (b) c=a m...

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