Home
Class 12
MATHS
If the line k^(2)(x-1)+k(y-2)+1=0 touche...

If the line `k^(2)(x-1)+k(y-2)+1=0` touches the parabola `y^(2)-4x-4y+8=0`, then k can be

A

-3

B

`-sqrt(5)`

C

`(7)/(19)`

D

1000

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
1,2,3,4
Given parabola is
`(y-2)^(2)=4(x-1)`
Equation of tangent having slope m is
`(y-2)=m(x-1)+(1)/(m)`
`orm^(2)(x-1)-m(y-2)+1=0`
`or(-m)^(2)(x-1)+(-m)(y-2)+1=0`
Comparing with given equation of tangent,
`kinR-{0}`
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

The fouce of the parabola x^(2)-6x+4y+1=0 is

The vertex of the parabola x^(2)-6x+4y+1=0 is

If the line x-1=0 is the directrix of the parabola y^2-k x+8=0 , then one of the values of k is (a) 1/8 (b) 8 (c) 4 (d) 1/4

The circle x ^(2) +y^(2) -8 x+4=0 touches -

The circle x^(2)+y^(2)+2lamdax=0,lamdainR , touches the parabola y^(2)=4x externally. Then,

If the area inside the parabola 5x^(2) -y=0 but outside the parabola 2x^(2) -y+ 9 =0 is 2K sqrt 3 sq . Units then the value of K is equal to-

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If the radius of the circle touching the pair of lines 7x^(2) - 18 xy +7y^(2) = 0 and the circle x^(2) +y^(2) - 8x - 8y = 0 , and contained in the given circle is equal to k, then k^(2) is equal to

If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k is (are)

If a straight line pasing through the focus of the parabola y^(2) = 4ax intersects the parabola at the points (x_(1), y_(1)) and (x_(2) , y_(2)) then prove that y_(1)y_(2)+4x_(1)x_(2)=0 .

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

    |