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If the parabola y=a x^2-6x+b passes thro...

If the parabola `y=a x^2-6x+b` passes through `(0,2)` and has its tangent at `x=3/2` parallel to the x-axis, then `a=2,b=-2` (b) `a=2,b=2` `a=-2,b=2` (d) `a=-2,b=-2`

A

a=2, b=-2

B

a=2, b=2

C

a=-2, b=2

D

a=-2, b=-2

Text Solution

Verified by Experts

The correct Answer is:
B
(2) `y=ax^(2)-6x+b` passes through (0,2). Here,
`2=a(0^(2))-6(0)+b`
`:." "b=2`
Also, `(dy)/(dx)=2ax-6`
`:." "((dy)/(dx))_(x=3//2)=2a((3)/(2))-6`
`or" "3a-6=0`
`:." "a=2`
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CENGAGE-PARABOLA-Exercise (Single)
  1. If y=2x-3 is tangent to the parabola y^2=4a(x-1/3), then a is equal to

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  2. The locus of the center of a circle which cuts orthogonally the parabo...

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  3. If the parabola y=a x^2-6x+b passes through (0,2) and has its tangent ...

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  4. Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at...

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  5. The tangent to y^(2)=ax make angles theta(1)andtheta(2) with the x-axi...

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  6. A tangent is drawn to the parabola y^2=4 x at the point P whose abscis...

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  7. The straight lines joining any point P on the parabola y^2=4a x to the...

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  8. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

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  9. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

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  10. If the locus of the middle of point of contact of tangent drawn to the...

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  11. If the bisector of angle A P B , where P Aa n dP B are the tangents to...

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  12. From a point A(t) on the parabola y^(2)=4ax, a focal chord and a tange...

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  13. The point of intersection of the tangents of the parabola y^(2)=4x dra...

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  14. The angle between the tangents to the parabola y^2=4a x at the points ...

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  15. y=x+2 is any tangent to the parabola y^2=8xdot The point P on this tan...

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  16. If y=m1x+c and y=m2x+c are two tangents to the parabola y^2+4a(x+a)=0 ...

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  17. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

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  18. Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the...

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  19. Radius of the circle that passes through the origin and touches the ...

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  20. The mirror image of the parabola y^2=4x in the tangent to the parab...

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