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 c=2, then the point of contact is

A

A. (3,3)

B

B. (2,2)

C

C. (6,6)

D

D. (4,4)

Text Solution

Verified by Experts

The correct Answer is:
D
(4) If c=2, then the point of contact is `(1//2a,1//4a+2)`.
Since it lies on the line y=x, we have
`(1)/(2a),(1)/(4a)+2`
`i.e," "a=(1)/(8)`
Therefore, the point of contact is (4,4)
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise MATRIX MATCH TYPE|5 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise NUMERICAL VALUE TYPE|32 Videos

  • PARABOLA

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

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

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

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

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

If the line x+y =1 is a tangent to the parabola y^(2)-y +x=0 , then the point of contact is-

If the line 2x+sqrt(6)y=2 is a tangent to the hyperbola x^(2)-2y^(2)=4 , then the coordinates of the point of contact are -

y=x+2 is any tangent to the parabola y^2=8xdot The point P on this tangent is such that the other tangent from it which is perpendicular to it is (a) (2,4) (b) (-2,0) (c) (-1,1) (d) (2,0)

Find the equation of the tangent to the parabola y^2=8x having slope 2 and also find the point of contact.

If the tangent to the parabola y= x^(2) + 6 at the point (1, 7) also touches the circle x^(2) + y^(2) + 16x + 12y + c =0 , then the coordinates of the point of contact are-

The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

The point of intersection of the tangents to the parabola y^(2)=4ax at the points t_(1) and t_(2) is -

CENGAGE PUBLICATION-PARABOLA-LINKED COMPREHENSION TYPE
  1. y=x is tangent to the parabola y=ax^(2)+c. If a=2, then the value o...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. find the area of triangle whose vertices are (3,8),(-4,2)and (5,1)

    Text Solution

    |

  5. If l and m are variable real number such that 5l^(2)+6m^(2)-4lm+3l=0, ...

    Text Solution

    |

  6. If ∣ vec a + vecb ∣=60,∣ vec a − vecb ∣=40 and ∣veca∣=22 th...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Two tangents on a parabola are x-y=0 and x+y=0. S(2,3) is the focus ...

    Text Solution

    |

  11. Two tangents on a parabola are x-y=0 and x+y=0. S(2,3) is the focus ...

    Text Solution

    |

  12. Two tangents on a parabola are x-y=0 and x+y=0. S(2,3) is the focus ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The focus of the parabola y = 2x^(2) + x is

    Text Solution

    |

  17. The focus of the parabola y = 2x^(2) + x is

    Text Solution

    |

  18. The focus of the parabola y = 2x^(2) + x is

    Text Solution

    |

  19. Consider the inequality, 9^(x)-a.3^(x)-a+3 le 0, where 'a' is a real p...

    Text Solution

    |

  20. Consider the inequality, 9^(x)-a.3^(x)-a+3 le 0, where 'a' is a real p...

    Text Solution

    |