Home
Class 11
MATHS
If the line x + y = 1 touches the parab...

If the line x + y = 1 touches the parabola `y^(2) = kx` , then the value of k is

A

4

B

-4

C

2

D

-2

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`x+y-1=0rArry=-x+1`
This will touch the parabola `y^(2)=kx,` if
`1=(k//4)/-1" [putting c=1, a=k/4 and m = -1 in c=a/m]"`
`rArr" "k=-4`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|66 Videos

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise SECTION-I (SOLVED MCQs EXAMPLE)|1 Videos

  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

If the line 2x - 3y = k touches the parabola y^(2) = 6 x , then the value of k is (i) (27)/(4) (ii) -(27)/(4) (iii) -27 (iv) 27

If the line x + y = 1 touches the parabola y^2-y + x = 0 , then the coordinates of the point of contact are:

If the line y=mx+c touches the parabola y^(2)=4a(x+a) , then

If the line y=mx+c touches the parabola y^(2)=4a(x+a) , then

If the line x+y=a touches the parabola y=x-x^2, then find the value of a .

If the line x+y=a touches the parabola y=x-x^2, then find the value of adot

The line 4x+6y+9 =0 touches the parabola y^(2)=4ax at the point

If the line y=m x+1 is tangent to the parabola y^2=4x , then find the value of m .

Show that the line x + y = 1 touches the parabola y = x-x ^(2).

If the line y=3x+lambda touches the hyperbola 9x^(2)-5y^(2)=45 , then the value of lambda is

OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Chapter Test
  1. If the line x + y = 1 touches the parabola y^(2) = kx , then the val...

    Text Solution

    |

  2. If y=2x+k is a tangent to the curve x^(2)=4y, then k is equal to

    Text Solution

    |

  3. The normal drawn at a point (a t1 2,-2a t1) of the parabola y^2=4a x m...

    Text Solution

    |

  4. The mid-point of the chord 2x+y-4=0 of the parabola y^(2)=4x is

    Text Solution

    |

  5. The two ends of latusrectum of a parabola are the points (3, 6) and (-...

    Text Solution

    |

  6. Prove that the locus of the middle points of all chords of the parabol...

    Text Solution

    |

  7. The focus of the parabola x^2-8x+2y+7=0 is

    Text Solution

    |

  8. The point of contact of the line x-2y-1=0 with the parabola y^(2)=2(x-...

    Text Solution

    |

  9. Find the number of distinct normals that can be drawn from (-2,1) to t...

    Text Solution

    |

  10. At what point on the parabola y^2=4x the normal makes equal angle with...

    Text Solution

    |

  11. Three normals to the parabola y^2= x are drawn through a point (C, O) ...

    Text Solution

    |

  12. The normal chord of a parabola y^2= 4ax at the point P(x1, x1) subten...

    Text Solution

    |

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

    Text Solution

    |

  14. The circles on the focal radii of a parabola as diameter touch: A) th...

    Text Solution

    |

  15. If the normals from any point to the parabola y^2=4x cut the line x=2 ...

    Text Solution

    |

  16. about to only mathematics

    Text Solution

    |

  17. The equation of the tangent to the parabola y^(2)=8x which is perpendi...

    Text Solution

    |

  18. the tangent drawn at any point P to the parabola y^2= 4ax meets the di...

    Text Solution

    |

  19. about to only mathematics

    Text Solution

    |

  20. The parabola y^(2)=4ax passes through the point (2,-6). Find the lengt...

    Text Solution

    |

  21. A variable circle passes through the fixed point (2, 0) and touches y-...

    Text Solution

    |