Home
Class 12
MATHS
y=x is tangent to the parabola y=ax^(2)+...

y=x is tangent to the parabola `y=ax^(2)+c`.
If (1,1) is the point of contact, then a is

A

`1//4`

B

`1//3`

C

`1//2`

D

`1//6`

Text Solution

Verified by Experts

The correct Answer is:
C
(3) If (1,1) is point of contact, then a=1/2.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise (Numerical)|28 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise (Multiple)|26 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|19 Videos

Similar Questions

Explore conceptually related problems

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is

y=3x is tangent to the parabola 2y=ax^2+ab . If (2,6) is the point of contact , then the value of 2a is

y=x is tangent to the parabola y=ax^(2)+c . If a=2, then the value of c is

If the line Ix+my+n=0 is a tangent to the parabola y^(2)=4ax, then locus of its point of contact is:

Show that the length of the tangent to the parabola y^2 = 4ax intercepted between its point of contact and the axis of the parabola is bisected by the tangent at the vertex.

Tangent to the parabola y=x^(2)+ax+1 at the point of intersection of the y-axis also touches the circle x^(2)+y^(2)=r^(2) . Also, no point of the parabola is below the x-axis. The minimum area bounded by the tangent and the coordinate axes is

Tangent to the parabola y=x^(2)+ax+1 at the point of intersection of the y-axis also touches the circle x^(2)+y^(2)=r^(2) . Also, no point of the parabola is below the x-axis. The slope of the tangents when the radius of the circle is maximum is

Tangent to the parabola y=x^(2)+ax+1 at the point of intersection of the y-axis also touches the circle x^(2)+y^(2)=r^(2) . Also, no point of the parabola is below the x-axis. The slope of the tangents when the radius of the circle is maximum is

CENGAGE-PARABOLA-Exercise (Comprehension)
  1. y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A...

    Text Solution

    |

  2. y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A...

    Text Solution

    |

  3. y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A...

    Text Solution

    |

  4. PQ is the double ordinate of the parabola y^(2)=4x which passes throug...

    Text Solution

    |

  5. PQ is the double ordinate of the parabola y^(2)=4x which passes throug...

    Text Solution

    |

  6. PQ is the double ordinate of the parabola y^(2)=4x which passes throug...

    Text Solution

    |

  7. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

    Text Solution

    |

  8. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

    Text Solution

    |

  9. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

    Text Solution

    |

  10. Consider one sides AB of a square ABCD in order on line y=2x-17, and o...

    Text Solution

    |

  11. Consider one sides AB of a square ABCD in order on line y=2x-17, and o...

    Text Solution

    |

  12. Tangent to the parabola y=x^(2)+ax+1 at the point of intersection of t...

    Text Solution

    |

  13. Tangent to the parabola y=x^(2)+ax+1 at the point of intersection of t...

    Text Solution

    |

  14. Tangent to the parabola y=x^(2)+ax+1 at the point of intersection of t...

    Text Solution

    |

  15. The locus of the circumcenter of a variable triangle having sides the ...

    Text Solution

    |

  16. The locus of the circumcenter of a variable triangle having sides the ...

    Text Solution

    |

  17. The locus of the circumcenter of a variable triangle having sides the ...

    Text Solution

    |

  18. y=x is tangent to the parabola y=ax^(2)+c. If (1,1) is the point of ...

    Text Solution

    |

  19. y=x is tangent to the parabola y=ax^(2)+c. If c=2, then the point of...

    Text Solution

    |

  20. Consider the parabola whose focus is at (0,0) and tangent at vertex is...

    Text Solution

    |