Home
Class 12
MATHS
Let L be a normal to the parabola y^2=4x...

Let L be a normal to the parabola `y^2=4x`.If L passes through the point (9,6) then L is given by

A

y-x+3=0

B

y+3x-33=0

C

y+x-15=0

D

y-2x+12=0

Text Solution

Verified by Experts

The correct Answer is:
A, C, D

1,3,4
`y^(2)=4x`
The eqution of normal is `y=mx-2m-m^(3)`.
It passes through (9,6). So,
`m^(3)-7m+6=0`
`or(m-1)(m-2)(m-3)=0`
`orm=1,2,-3`
`:." normal are "y-x+3=0,y+3x-33=0,0y-2x+12=0`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Single Correct Answer Type|46 Videos
  • PARABOLA

    CENGAGE|Exercise Multiple Correct Answers Type|10 Videos
  • PARABOLA

    CENGAGE|Exercise JEE Main Previous Year|8 Videos
  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos
  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|19 Videos

Similar Questions

Explore conceptually related problems

Equation of the other normal to the parabola y^(2)=4x which passes through the intersection of those at (4,-4) and (9,-6) is

Equation of a normal to the parabola y^(2)=32x passing through its focus is lx+my+n=0 then l+m+n=

Let L be a tangent line to the parabola y^(2)=4x - 20 at (6, 2). If L is also a tangent to the ellipse (x^(2))/(2)+(y^(2))/(b)=1 , then the value of b is equal to :

If L is the length of the latus rectum of the hyperbola for which x=3 and y=2 are the equations of asymptotes and which passes through the point (4,6), then the value of (L)/(sqrt(2)) is

Let L_1 be a tangent to the parabola y^(2) = 4(x+1) and L_2 be a tangent to the parabola y^(2) = 8(x+2) such that L_1 and L_2 intersect at right angles. Then L_1 and L_2 meet on the straight line :

Let L be the length of the normal chord of the parabola y^(2)=8x which makes an angle pi//4 with the axis of x , then L is equal to (sqrt2=1.41)

The line l_(1) passing through the point (1,1) and the l_(2), passes through the point (-1,1) If the difference of the slope of lines is 2. Find the locus of the point of intersection of the l_(1) and l_(2)

Let L be the line passing through the point P (1, 2) such that its intercepted segment between the coordinate axes is bisected at P. If L_(1) is the line perpendicular to L and passing through the point (-2, 1) , then the point of intersection of L and L_(1) is :

Let L be the line passing through the point P (1,2) such that its intercepted segment between the co-ordinate axes is bisected at P. If L_(1) is the line perpendicular to L and psssing through the point (-2,1), then the point of intersection of L and L_(1) is

CENGAGE-PARABOLA-JEE Advenced Single Answer Type
  1. Let (x,y) be any point on the parabola y^2 = 4x. Let P be the point t...

    Text Solution

    |

  2. The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = ...

    Text Solution

    |

  3. The tangent PT and the normal PN to the parabola y^2=4ax at a point P...

    Text Solution

    |

  4. Let A and B be two distinct points on the parabola y^2 = 4x. If the ax...

    Text Solution

    |

  5. Let L be a normal to the parabola y^2=4x.If L passes through the point...

    Text Solution

    |

  6. Let P and Q be distinct points on the parabola y^2 = 2x such that a c...

    Text Solution

    |

  7. Let P be the point on parabola y^2=4x which is at the shortest distanc...

    Text Solution

    |

  8. The circle C(1):x^(2)+y^(2)=3, with centre at O, intersects the parabo...

    Text Solution

    |

  9. If a chord, which is not a tangent, of the parabola y^(2)=16x has the ...

    Text Solution

    |

  10. Let PQ be a focal chord of the parabola y^2 = 4ax The tangents to the ...

    Text Solution

    |

  11. Let PQ be a focal chord of the parabola y^(2)=4ax. The tangents to the...

    Text Solution

    |

  12. Let a, r, s, t be non-zero real numbers. Let P(at^2, 2at), Q, R(ar^2, ...

    Text Solution

    |

  13. Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2a...

    Text Solution

    |

  14. A line L : y = mx + 3 meets y-axis at E (0, 3) and the arc of the para...

    Text Solution

    |

  15. Consider the parabola y^2 = 8x. Let Delta1 be the area of the triangle...

    Text Solution

    |

  16. Let S be the focus of the parabola y^2=8x and let PQ be the common cho...

    Text Solution

    |

  17. Let the curve C be the mirror image of the parabola y^2 = 4x with resp...

    Text Solution

    |

  18. ·If the normals of the parabola y^2=4x drawn at the end points of it...

    Text Solution

    |