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If the points A (1,3) and B (5,5) lying ...

If the points A (1,3) and B (5,5) lying on a parabola are equidistant from focus, then the slope of the directrix is

A

`(1)/(2)`

B

`-(1)/(2)`

C

2

D

-2

Text Solution

Verified by Experts

The correct Answer is:
A
(1) Since points A and B are equidistant from focus, line AB is perpendicular to axis and so, parallel to directrix.
`:.` Slope of directrix = Slope of AB `=(5-3)/(5-1)=(1)/(2)`
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CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. The circle x^(2)+y^(2)+2lamdax=0,lamdainR, touches the parabola y^(2)=...

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  2. A set of parallel chords of the parabola y^2=4a x have their midpoint ...

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  3. If the points A (1,3) and B (5,5) lying on a parabola are equidistant ...

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  4. The radius of the circle whose centre is (-4,0) and which cuts the par...

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  5. The circle x^2+y^2=5 meets the parabola y^2=4x at P and Q . Then the l...

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  6. If y(1),y(2),andy(3) are the ordinates of the vertices of a triangle i...

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  7. let P be the point (1, 0) and Q be a point on the locus y^2= 8x. The l...

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  8. An equilateral triangle is inscribed in the parabola y^(2)=4ax, such...

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  9. C is the centre of the circle with centre (0,1) and radius unity. y=ax...

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  10. P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) ...

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  11. AB is a chord of the parabola y^2 = 4ax with its vertex at A. BC is dr...

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  12. Set of value of alpha for which the point (alpha,1) lies inside the ci...

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  13. If X is the foot of the directrix on the a parabola. PP' is a double o...

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  14. A water jet from a function reaches it maximum height of 4 m at a d...

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  15. Area of the triangle formed by the vertex, focus and one end of latusr...

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  16. The locus of the vertex of the family of parabolas y=(a^3x^2)/3+(a^(2x...

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  17. Two parabola have the same focus. If their directrices are the x-axis ...

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  18. The locus of the point (sqrt(3h),sqrt(3k+2)) if it lies on the line x-...

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  19. A circle touches the x-axis and also touches the circle with centre (0...

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  20. If parabolas y^2=lambdax and 25[(x-3)^2+(y+2)^2]=(3x-4y-2)^2 are equal...

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