Home
Class 12
MATHS
Which of the following line can be norma...

Which of the following line can be normal to parabola `y^2=12 x ?` `x+y-9=0` (b) `2x-y-32=0` `2x+y-36=0` (d) `3x-y-72=0`

A

x+y-9=0

B

2x-y-32=0

C

2x+y-36=0

D

3x-y-99=0

Text Solution

Verified by Experts

The correct Answer is:
A, C, D

1,3,4 The equation of normal to the parabola `y^(2)=12x` having slope m is `y=mx-6m-3m^(3)`. Options (1), (3) and (4) are normal for m=-1,-2, and 3, respectively.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise LINKED COMPREHENSION TYPE|45 Videos
  • PARABOLA

    CENGAGE PUBLICATION|Exercise MATRIX MATCH TYPE|5 Videos
  • PARABOLA

    CENGAGE PUBLICATION|Exercise EXERCISE (SINGLE CORRECT ANSWER TYPE )|98 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

Which of the following line can be tangent to the parabola y^2=8x ? x-y+2=0 (b) 9x-3y+2=0 x+2y+8=0 (d) x+3y+12=0

Which of the following lines have the intercepts of equal lengths on the circle, x^2+y^2-2x+4y=0 (A) 3x -y= 0 (B) x+3y=0 (C) x+3y+10=0 (D) 3x-y-10=0

The line 2x+y+lamda=0 is a normal to the parabola y^(2)=8x, is lamda =

The lines parallel to the normal to the curve x y=1 is/are (a) 3x+4y+5=0 (b) 3x-4y+5=0 (c) 4x+3y+5=0 (d) 3y-4x+5=0

Which of the following is a point on the common chord of the circle x^2+y^2+2x-3y+6=0 and x^2+y^2+x-8y-13=0? (1,-2) (b) (1,4) (c) (1,2) (d) (1,-4)

Find the area bounded by the parabola y^2=9x and the straight line x-y+2=0

Find the equation of line which is normal to the parabola x^(2)=4y and touches the parabola y^(2)=12x .

(6,0),(0,6),a n d(7,7) are the vertices of a A B C . The incircle of the triangle has equation. (a) x^2+y^2-9x-9y+36=0 (b) x^2+y^2+9x-9y+36=0 (c) x^2+y^2+9x+9y-36=0 (d) x^2+y^2+18 x-18 y+36=0

The equation of tangent to hyperbola 4x^2-5y^2=20 which is parallel to x-y=2 is (a) x-y+3=0 (b) x-y+1=0 (c) x-y=0 (d) x-y-3=0

If 2x+y+lambda=0 is a normal to the parabola y^2=-8x , then lambda is (a)12 (b) -12 (c) 24 (d) -24

CENGAGE PUBLICATION-PARABOLA-EXERCISE (MULTIPLE CORRECT ANSWER TYPE )
  1. The locus of the midpoint of the focal distance of a variable point ...

    Text Solution

    |

  2. A square has one vertex at the vertex of the parabola y^2=4a x and the...

    Text Solution

    |

  3. If two distinct chords of a parabola y^2=4ax , passing through (a,2a) ...

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

  5. If the parabola x^2=ay makes an intercept of length sqrt40 unit on the...

    Text Solution

    |

  6. The equation of the directrix of the parabola with vertex at the origi...

    Text Solution

    |

  7. Tangent is drawn at any point (x1, y1) other than the vertex on the pa...

    Text Solution

    |

  8. The parabola y^2=4x and the circle having its center at (6, 5) interse...

    Text Solution

    |

  9. Which of the following line can be tangent to the parabola y^2=8x ? x...

    Text Solution

    |

  10. If the line k^(2)(x-1)+k(y-2)+1=0 touches the parabola y^(2)-4x-4y+8=0...

    Text Solution

    |

  11. The equation of a circle of radius 1 touching the circles x^2+y^2-2|x|...

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. The line x+ y +2=0 is a tangent to a parabola at point A, intersect t...

    Text Solution

    |

  14. Which of the following line can be normal to parabola y^2=12 x ? x+y-...

    Text Solution

    |

  15. A normal drawn to the parabola y^2=4a x meets the curve again at Q suc...

    Text Solution

    |

  16. A circle is drawn having centre at C (0,2) and passing through focus ...

    Text Solution

    |

  17. From any point P on the parabola y^(2)=4ax, perpebdicular PN is drawn ...

    Text Solution

    |

  18. Let P be the point (1,0) and Q be a point on the locus y^(2)=8x. The l...

    Text Solution

    |

  19. The value(s) of a for which two curves y=ax^(2)+ax+(1)/(24)andx=ay^(2)...

    Text Solution

    |

  20. From any point P on the parabola y^(2)=4ax, perpebdicular PN is drawn ...

    Text Solution

    |