Home
Class 12
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)+m_(1)m_(2)=0`

B

`m_(1)+m_(2)-m_(1)m_(2)=2/3`

C

`m_(1)+m_(2)+2m_(1)m_(2)=1/3`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Let equation of tangent is `y=mx+a/m`
`implies-a=-3am+a/m`
`implies3m^(2)-m-1=0`
`m_(1)+m_(2)=1/3,m_(1),m_(2)=-1/3`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE ENGLISH|Exercise Math|105 Videos

  • TEST PAPER

    RESONANCE ENGLISH|Exercise MATHEMATICS|48 Videos

  • TEST SERIES

    RESONANCE ENGLISH|Exercise MATHEMATICS|132 Videos

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+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 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 (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

RESONANCE ENGLISH-TEST PAPERS-MATHEMATICS
  1. For the curve y=4x^3-2x^5, find all the points at which the tangents p...

    Text Solution

    |

  2. Minimum value of (sin^(-1)x)^(2)+(cos^(-1)x)^(2) is greater than

    Text Solution

    |

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

    Text Solution

    |

  4. f(x)=lim(mrarroo){lim(nrarroo)cos^(2m)n!pix} then

    Text Solution

    |

  5. Tangents are drawn to the hyperbola x^2/9-y^2/4=1 parallet to the srai...

    Text Solution

    |

  6. Q. For every integer n, leta(n) and b(n) be real numbers. Let functio...

    Text Solution

    |

  7. Let a and b are real numbers such that the function f(x)={(-3ax^(2)-2,...

    Text Solution

    |

  8. If both Lim(xrarrc^(-))f(x) and Lim(xrarrc^(+))f(x) exist finitely and...

    Text Solution

    |

  9. If both Lim(xrarrc^(-))f(x) and Lim(xrarrc^(+))f(x) exist finitely and...

    Text Solution

    |

  10. In a A B C ,A-=(alpha,beta),B-=(1,2),C-=(2,3), point A lies on the li...

    Text Solution

    |

  11. In a Delta ABC, A -= (alpha, beta), B -= (1, 2), C -= (2,3) and point ...

    Text Solution

    |

  12. Let f(x) be real valued continuous function on R defined as f(x)=x^(2)...

    Text Solution

    |

  13. Let f(x) be a real valued continuous function on R defined as f(x)=...

    Text Solution

    |

  14. Let all chords of parabola y^(2)=x+1 which subtends right angle at (1,...

    Text Solution

    |

  15. lim(xrarr(pi)/2)(1-sinxsin3xsin5x.sin7x)/(((pi)/2-x)^(2)) is k then k/...

    Text Solution

    |

  16. If derivative of y=|x-1|^(sinx) at x=-(pi)/2 is (1+api)^(b) then value...

    Text Solution

    |

  17. sin^(-1)(sin10) is a+bpi then |a+b| is

    Text Solution

    |

  18. f:[0,2pi]rarr[-1,1] and g:[0,2pi]rarr[-1,1] be respectively given by f...

    Text Solution

    |

  19. If solution of cot(sin^(-1)sqrt(1-x^(2)))=sin(tan^(-1)(xsqrt(6))),x!=0...

    Text Solution

    |

  20. about to only mathematics

    Text Solution

    |