Home
Class 12
MATHS
Two straight lines (y-b)=m1(x+a) and (y-...

Two straight lines `(y-b)=m_1(x+a)` and `(y-b)=m_2(x+a)` are the tangents of `y^2=4a xdot` Prove `m_1m_2=-1.`

A

`m_1+m_2=0`

B

`m_1m_2=1`

C

`m_1m_2= -1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise LEVEL - 2|111 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|15 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 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

Let the lines (y-2)=m_1(x-5) and (y+4)=m_2(x-3) intersect at right angles at P (where m_1 and m_2 are parameters). If the locus of P is x^2+y^2+gx+fy+7=0 , then the value of |f+g| is__________

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 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

The straight lines represented by (y-m x)^2=a^2(1+m^2) and (y-n x)^2=a^2(1+n^2) from a (a) rectangle (b) rhombus (c) trapezium (d) none of these

The straight lines represented by (y-m x)^2=a^2(1+m^2) and (y-n x)^2=a^2(1+n^2) from a (a)rectangle (b) rhombus (c)trapezium (d) none of these

A triangle has two sides y=m_1x and y=m_2x where m_1 and m_2 are the roots of the equation b alpha^2+2h alpha +a=0 . If (a,b) be the orthocenter of the triangle, then find the equation of the third side in terms of a , b and h .

STATEMENT-1: The straight lines 2x+3y+5=0and 3x-2y+1=0 are perpendicular to each other. STATEMENT-2: Two lines y=m_(1)x+c_(1)and y=m_(2)x+c_(2) where m_(1),m_(2)in R are perpendicular if m_(1),m_(2)=-1. STATEMENT-2: Two lines y=m_(1)xx+x_(1)and y=m_(2)x+c_(2)where m_(1),m_(2)inR are peprendicular if m_(1)m_(2)=-1.

VMC MODULES ENGLISH-CONIC SECTIONS-LEVEL - 1
  1. If the line px + qy =1m is a tangent to the parabola y^(2) =4ax, then

    Text Solution

    |

  2. The point of contact of the tangent of y^2=2x inclined to 45^(@) to th...

    Text Solution

    |

  3. Two straight lines (y-b)=m1(x+a) and (y-b)=m2(x+a) are the tangents of...

    Text Solution

    |

  4. The locus of the intersection points of pair of perpendicular tangents...

    Text Solution

    |

  5. If the tangents at the points Pa n dQ on the parabola y^2=4a x meet at...

    Text Solution

    |

  6. Consider a curve C : y^2-8x-2y-15=0 in which two tangents T1a n dT2 ar...

    Text Solution

    |

  7. If a tangent to the parabola y^2=4a x meets the x-axis at T and inters...

    Text Solution

    |

  8. Let N be the foot of perpendicular to the x-axis from point P on the p...

    Text Solution

    |

  9. AB, AC are tangents to a parabola y^2=4ax; p1, p2, p3 are the lengths...

    Text Solution

    |

  10. If t is the parameter for one end of a focal chord of the parabola y^2...

    Text Solution

    |

  11. set of values of m for which a chord of slope m of the circle x^2 + y^...

    Text Solution

    |

  12. y=2x+c, 'c' being variable is a chord of the parabola y^2=4x, meeting ...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. If the line y=mx+c is a normal to the parabola y^2=4ax, then c is

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

  16. From a point (h,k) three normals are drawn to the parabola y^2=4ax. Ta...

    Text Solution

    |

  17. From a point (h,k) three normals are drawn to the parabola y^2=4ax. Ta...

    Text Solution

    |

  18. From a point (h,k) three normals are drawn to the parabola y^2=4ax. Ta...

    Text Solution

    |

  19. From a point (h,k) three normals are drawn to the parabola y^2=4ax. Ta...

    Text Solution

    |

  20. Let A and B be two points on y^(2)=4ax such that normals to the curve ...

    Text Solution

    |