Home
Class 12
MATHS
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) `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`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE ENGLISH|Exercise EXERCISE (MULTIPLE CORRECT ANSWER TYPE )|26 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise LINKED COMPREHENSION TYPE|45 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise Concept Applications Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE ENGLISH|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE ENGLISH|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

If the curve y=a x^2-6x+b pass through (0,2) and has its tangent parallel to the x-axis at x=3/2, then find the values of aa n dbdot

If the curve y=a x^2-6x+b pass through (0,2) and has its tangent parallel to the x-axis at x=3/2, then find the values of a and bdot

If (a , b) is the midpoint of a chord passing through the vertex of the parabola y^2=4x , then (a) a=2b (b) a^2=2b (c) a^2=2b (d) 2a=b^2

If x=asectheta and y=btantheta , then b^2x^2-a^2y^2= (a) a b (b) a^2-b^2 (c) a^2+b^2 (d) a^2b^2

The tangent to y=a x^2+b x+7/2a t(1,2) is parallel to the normal at the point (-2,2) on the curve y=x^2+6x+10 , then a=-1 b. a=1 c. b=5/2 d. b=-5/2

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then (a) d^2+(2b+3c)^2=0 (b) d^2+(3b+2c)^2=0 (c) d^2+(2b-3c)^2=0 (d)none of these

If a circle passes through the point (a, b) and cuts the circle x^2 + y^2 = 4 orthogonally, then the locus of its centre is (a) 2ax+2by-(a^(2)+b^(2)+4)=0 (b) 2ax+2by-(a^(2)-b^(2)+k^(2))=0 (c) x^(2)+y^(2)-3ax-4by+(a^(2)+b^(2)-k^(2))=0 (d) x^(2)+y^(2)-2ax-3by+(a^(2)-b^(2)-k^(2))=0

The hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (2, ) and has the eccentricity 2. Then the transverse axis of the hyperbola has the length 1 (b) 3 (c) 2 (d) 4

Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at the vertex of the parabola. Then the tangents drawn to the parabola at A .and B will intersect at (a) (-4a ,0) (b) (-2a ,0) (-3a ,0) (d) none of these

If x=acostheta and y=bsintheta , then b^2x^2+a^2y^2= (a) a^2b^2 (b) a b (c) a^4\ b^4 (d) a^2+b^2

CENGAGE ENGLISH-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. If y=2x-3 is tangent to the parabola y^2=4a(x-1/3), then a is equal to...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. find the equation of hyperabola where foci are (0,12) and (0,-12)and t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. The point of intersection of the tangents of the parabola y^2=4x drawn...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |