Home
Class 11
MATHS
If y + b = m(1)(x + a) and y + b = m(2)(...

If `y + b = m_(1)(x + a)` and `y + b = m_(2)(x+a)` are two tangents to the parabola `y^(2) =4ax`, then

A

`m_(1)+m_(2)=0`

B

`m_(1)+m_(2)= 1`

C

`m_(1)m_(2) = -1`

D

`m_(1)=m_(2)`

Text Solution

Verified by Experts

The correct Answer is:
C

`x+a=0`
As we know that, tangent are drawn any point on the directrix arc at right angle
`m_(1)m_(2)= -1`
Promotional Banner

Similar Questions

Explore conceptually related problems

If y+b=m_1(x+a) and y+b=m_2(x+a) are two tangents to the paraabola y^2=4ax then

Statement-1: y+b=m_(1) (x+a) and y+b=m_(2)(x+a) are perpendicular tangents to the parabola y^(2)=4ax . Statement-2: The locus of the point of intersection of perpendicular tangents to a parabola is its directrix.

If the line px + qy =1m is a tangent to the parabola y^(2) =4ax, then

The common tangent to the parabola y^2=4ax and x^2=4ay is

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y_2=8x , then (a) m_1+m_2=0 (b) m_1+m_2=-1 (c) m_1+m_2=1 (d) none of these

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+c)=0 , then m_1+m_2=0 (b) 1+m_1+m_2=0 m_1m_2-1=0 (d) 1+m_1m_2=0

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+a)=0 , then (a) m_1+m_2=0 (b) 1+m_1+m_2=0 (c) m_1m_2-1=0 (d) 1+m_1m_2=0

If (x_(1),y_(1)) and (x_(2),y_(2)) are the ends of a focal chord of the parabola y^(2) = 4ax then show that x_(1)x_(2)=a^(2),y_(1)y_(2)= -4a^(2)

If the line y=m x+1 is tangent to the parabola y^2=4x , then find the value of m .

If the line y=m x+1 is tangent to the parabola y^2=4x , then find the value of mdot

VMC MODULES ENGLISH-QUIZ-Mathematics
  1. If the normals drawn at the points t(1) and t(2) on the parabola meet ...

    Text Solution

    |

  2. A tangent to the parabola y^2=8x makes an angle of 45^0 with the strai...

    Text Solution

    |

  3. The equation of the tangent to the parabola y^(2) =9x, which passes th...

    Text Solution

    |

  4. The vertex of the parabola y^(2) =(a-b)(x -a) is

    Text Solution

    |

  5. The curve is given by x = cos 2t, y = sin t represents

    Text Solution

    |

  6. If b,k are intercepts of a focal chord of the parabola y 2 =4ax then...

    Text Solution

    |

  7. vertex and focus of a parabola are (-1,1) and (2,3) respectively. find...

    Text Solution

    |

  8. The equation of the tangent to the parabola y^(2) =9x, which passes th...

    Text Solution

    |

  9. If y + b = m(1)(x + a) and y + b = m(2)(x+a) are two tangents to the p...

    Text Solution

    |

  10. If the chord of contact of tangents from a point P to the parabola y^2...

    Text Solution

    |

  11. Find the number of distinct normals that can be drawn from (-2,1) to t...

    Text Solution

    |

  12. If the segment intercepted by the parabola y=4a x with the line l x+m ...

    Text Solution

    |

  13. The co-ordinates of foci of an ellipse 3x^(2)+4y^(2)+12x+16y-8=0 is :

    Text Solution

    |

  14. In an ellipse the distance between the foci is 8 and the distance betw...

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

  16. The function f(x) = x^(2) - 3x + 7 is an example of

    Text Solution

    |

  17. For a signum function f(x), the value of f(x) at x = -4 is

    Text Solution

    |

  18. The largest set of real values of x for which f(x) = sqrt((x+2)(5-x)) ...

    Text Solution

    |

  19. The domain of the function f(x) = log(3/2) log(1/2)logpi log(pi/4) x ...

    Text Solution

    |

  20. Domain of definition of the function f(x)=(9)/(9-x^(2)) +log(10) (x^...

    Text Solution

    |