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If the line x-1=0 is the directrix of th...

If the line `x-1=0` is the directrix of the parabola `y^2-k x+8=0` , then one of the values of `k` is `1/8` (b) 8 (c) 4 (d) `1/4`

A

-8

B

`1//8`

C

`1//4`

D

4

Text Solution

Verified by Experts

The correct Answer is:
A, D
1,4
We have equation of parabola,
`y^(2)=kx-8ory^(2)=k(x-(8)/(k))`
Equation of directrix is
`x-(8)/(k)=-(k)/(4)orx=-(k)/(4)+(8)/(k)`
Given equation of directrix is x=1.
`:.(8)/(k)-(k)/(4)=1`
`rArrk^(2)+4k-32=0`

`rArr(k-4)(k+8)=0`
`rArrk=-8,4`
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CENGAGE-PARABOLA-Exercise (Multiple)
  1. If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k ...

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  2. If the line x-1=0 is the directrix of the parabola y^2-k x+8=0 , then ...

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  3. The extremities of latus rectum of a parabola are (1, 1) and (1,-1) . ...

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  4. The value(s) of a for which two curves y=ax^(2)+ax+(1)/(24)andx=ay^(2)...

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  5. In which of the following cases, a unique parabola will be obtained ?

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  6. A quadrilateral is inscribed in a parabola . Then,

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  7. The locus of the midpoint of the focal distance of a variable point ...

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  8. A square has one vertex at the vertex of the parabola y^2=4a x and the...

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  9. If two distinct chords of a parabola y^2=4ax , passing through (a,2a) ...

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  10. Let PQ be a chord of the parabola y^2=4x. A circle drawn with PQ as a...

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  11. If the parabola x^2=ay makes an intercept of length sqrt40 unit on the...

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  12. The equation of the directrix of the parabola with vertex at the origi...

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  13. Tangent is drawn at any point (x1, y1) other than the vertex on the pa...

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  14. The parabola y^2=4x and the circle having its center at 6, 5) intersec...

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  15. Which of the following line can be tangent to the parabola y^2=8x ? x...

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  16. If the line k^(2)(x-1)+k(y-2)+1=0 touches the parabola y^(2)-4x-4y+8=0...

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  17. The equation of the line that touches the curves y=x|x| and x^2+(y^2-2...

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  18. The equations of the common tangents to the parabola y = x^2 and y=-...

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  19. The line x+ y +2=0 is a tangent to a parabola at point A, intersect t...

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  20. Which of the following line can be normal to parabola y^2=12 x ? x+y-...

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