Home
Class 12
MATHS
Two straight lines are perpendicular to ...

Two straight lines are perpendicular to each other. One of them touches the parabola `y^2=4a(x+a)` and the other touches `y^2=4b(x+b)` . Their point of intersection lies on the line. (a)`x-a+b=0` (b) `x+a-b=0` (c)`x+a+b=0` (d) `x-a-b=0`

A

`(a-x)(x+b)-ay=0`

B

`(a+x)(x-b)-ab=((a+x)(x-b))^2`

C

`(a+x)(b-x)-ay=ab`

D

`(a+x)(x-b)-ab={ab-(a+x)(x-b)}^2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

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

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE MAIN ARCHIVE|15 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise LEVEL - 1|178 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

Prove that the line x/l+y/m=1 touches the parabola y^2=4a(x+b) , if m^2(l+b)+al^2=0 .

The point of intersection of the tangents of the parabola y^2=4x drawn at the endpoints of the chord x+y=2 lies on (a) x-2y=0 (b) x+2y=0 (c) y-x=0 (d) x+y=0

The angle between the tangents to the parabola y^2=4a x at the points where it intersects with the line x-y-a=0 is (a) pi/3 (b) pi/4 (c) pi (d) pi/2

The planes x=0 and y=0 (A) are parallel (B) are perpendicular to each other (C) interesect in z-axis (D) none of these

Let the curve C be the mirror image of the parabola y^2 = 4x with respect to the line x+y+4=0 . If A and B are the points of intersection of C with the line y=-5 , then the distance between A and B is

Prove that the line x/a + y/b =1 and x/b - y/a =1 are perpendicular to each other.

The straight lines joining any point P on the parabola y^2=4a x to the vertex and perpendicular from the focus to the tangent at P intersect at Rdot Then the equation of the locus of R is (a) x^2+2y^2-a x=0 (b) 2x^2+y^2-2a x=0 (c) 2x^2+2y^2-a y=0 (d) 2x^2+y^2-2a y=0

Find the equation of the line passing through the point of intersection of the lines x+5y+7=0 and 3x+2y-5=0 (b) perpendicular to the line 7x + 2y - 5 = 0

The point on the line x-y+ 2= 0 from which the tangent to the parabola y^2= 8x is perpendicular to the given line is (a, b) , then the line ax + by+c=0 is

The two lines represented by 3a x^2+5x y+(a^2-2)y^2=0 are perpendicular to each other for (a) two values of a (b) a (c) for one value of a (d) for no values of a

VMC MODULES ENGLISH-CONIC SECTIONS-LEVEL - 2
  1. P is parabola y^2=4ax and locus of mid points of all chords of this pa...

    Text Solution

    |

  2. Foot of the directrix of the parabola y^(2) = 4ax is the point

    Text Solution

    |

  3. Two straight lines are perpendicular to each other. One of them touche...

    Text Solution

    |

  4. P is parabola y^2=4ax and locus of mid points of all chords of this pa...

    Text Solution

    |

  5. A line bisecting the ordinate PN of a point P(at^2,2at),t gt 0 , on th...

    Text Solution

    |

  6. If P, Q, R are three points on a parabola y^2=4ax whose ordinates are ...

    Text Solution

    |

  7. about to only mathematics

    Text Solution

    |

  8. The tangent at the point P(x1, y1) to the parabola y^2 = 4 a x meets t...

    Text Solution

    |

  9. Find the equations of the common tangents to the circle x^2+y^2 = 8 an...

    Text Solution

    |

  10. If the normal at any point P on the ellipse cuts the major and mirror ...

    Text Solution

    |

  11. Prove that the focus of id-points of the portion of the tamgents to th...

    Text Solution

    |

  12. The tangent and normal to the ellipse x^2+4y^2=4 at a point P(theta) o...

    Text Solution

    |

  13. The line passing through the extremity A of the major exis and extremi...

    Text Solution

    |

  14. about to only mathematics

    Text Solution

    |

  15. If the normal at an end oof a lasrurectum of an ellipse x^(2)/a^(2)+y^...

    Text Solution

    |

  16. The points of intersection of the two ellipses x^2+2y^2-6x-12y + 23 = ...

    Text Solution

    |

  17. If l is the length of the intercept made by a common tangent to the ci...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. The locus of the mid-points of chords of ellipse, the tangents at the ...

    Text Solution

    |

  20. If a variable straight line x cos alpha+y sin alpha=p which is a chord...

    Text Solution

    |