Home
Class 12
MATHS
Tangent to the parabola y=x^(2)+ax+1 at ...

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

A

(a) -1

B

(b) 1

C

(c) 0

D

(d) 2

Text Solution

Verified by Experts

The correct Answer is:
C
(3) The equation of the tangent at (0,1) to the parabola
`y=x^(2)+ax+1` is
y-1=a(x-0)
`orax-y+1=0`
As it touches the circle, we get
`r=(1)/(sqrt(a^(2)+1))`
The radius is maximum when a=0.
Therefore, the equation of the tangent is y=1.
Therefore, the slope of the tangent is 0.
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

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 radius of circle when a attains its maximum value is

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

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 equations of the two common tangents to the circle x^(2) +y^(2)=2a^(2) and the parabola y^(2)=8ax are-

Obtain the locus of the point of intersection of the tangent to the circle x^2 + y^2 = a^2 which include an angle alpha .

The angle between tangents to the parabola y^2=4ax at the points where it intersects with teine x-y-a = 0 is (a> 0)

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Let PQ be a focal chord of the parabola y^2 = 4ax The tangents to the ...

    Text Solution

    |

  9. Let PQ be a focal chord of the parabola y^(2)=4ax. The tangents to the...

    Text Solution

    |

  10. Let a, r, s, t be non-zero real numbers. Let P(at^2, 2at), Q, R(ar^2, ...

    Text Solution

    |

  11. Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2a...

    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=2ax^(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

    |