Home
Class 12
MATHS
The slope of line which belongs to famil...

The slope of line which belongs to family (1+ l) x + (l-1)y + 2(1-l) = 0 and makes shortest intercept on `x^2 = 4y - 4` is :

Text Solution

Verified by Experts

The correct Answer is:
0
0 The family of lines `(1+lamda)x+(lamda-1)y+2(1-lamda)=0` is concurrent at (0,2). The focus of the parabola `x^(2)=4(y-1)` is (0,2).
Now, the shortest intercept of the line on the parabola which passes through the focus is latus rectum.
The axis of the given parabola is the y-axis.
Therefore, the latus rectum is parallel to the x-axis.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ARCHIVES SINGLE CORRECT ANSWER TYPE|8 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise JEE ADVENCED SINGLE CORRECT ANSWER TYPE|2 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise MATRIX MATCH TYPE|5 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 slope and y - intercept of the line 2x-3y +5=0 are -

Find the equation of the straight line which passes through the point of intercestion of the straight lines 3x-4y+1=0 and 5x+y=0 and makes equal intercepts upon the coordinate axes .

Equation of a line in the plane pi =2x-y+z-4=0 which is perpendicular to the line l whose equation is (x-2)/1=(y-2)/(-1)=(z-3)/(-2) and which passes through the point of intersection of l and pi is (A) (x-2)/1=(y-1)/5=(z-1)/(-1) (B) (x-1)/3=(y-3)/5=(z-5)/(-1) (C) (x+2)/2=(y+1)/(-1)=(z+1)/1 (D) (x-2)/2=(y-1)/(-1)=(z-1)/1

Equation of a line is 3x - 4y + 10 = 0 . Find its (i) slope , (ii) x - and y - intercepts.

The coordinates of a point on the line x + y + 1 = 0 which is at a distance sqrt(2) units from the line 3x + 4y - 2 = 0 are

Let l be the line belonging to the family of straight lines (a + 2b)x+ (a - 3b)y +a-8b = 0, a, b in R , which is farthest from the point (2, 2), then area enclosed by the line L and the coordinate axes is

Let L be the line belonging to the family of straight lines (a+2b) x+(a-3b)y+a-8b =0, a, b in R, which is the farthest from the point (2, 2). If L is concurrent with the lines x-2y+1=0 and 3x-4y+ lambda=0 , then the value of lambda is

If 7l^2 - 9m^2 + 8l + 1 = 0 and we have to find equation of circle having lx + my + 1 = 0 is a tangent and we can adjust given condition as 16l^2 + 8l + 1 = 9(l^2 + m^2) or (4l^2 + 1)^2 = 9(l^2 + m^2) implies |4l + 1|/sqrt ((l^2 + m^2)) = 3 Centre of circle = (4, 0) and radius = 3 when any two non parallel lines touching a circle, then centre of circle lies on angle bisector of lines. Answer the following question based on above passage : If 16m^2 - 8l - 1 = 0 , then equation of the circle having lx + my + 1 = 0 is a tangent is

A(x_1,y_1),B(x_2,y_2),C(x_3,y_3) are the vertices of a triangle ABC. lx+my+n=0 is an equation of the line L. Answer the following questions based on above passage : If the centroid of the triangle ABC is at the origin and algebraic sum of the length of the perpendiculars from the vertices of the triangle ABC on the line L is equal to 1 then sum of the squares of the intercepts made by L on the coordinate axes is equal to

Show that the lines 4x+y-9=0,x-2y+3=0,5x-y-6=0 make equal intercepts on any line of slope 2.

CENGAGE PUBLICATION-PARABOLA-NUMERICAL VALUE TYPE
  1. From the point (-1,2), tangent lines are to the parabola y^(2)=4x. If ...

    Text Solution

    |

  2. Line y=2x-b cuts the parabola y=x^(2)-4x at points A and B. Then the v...

    Text Solution

    |

  3. A line through the origin intersects the parabola 5y=2x^(2)-9x+10 at t...

    Text Solution

    |

  4. IF the circle (x-6)^2+y^2=r^2 and the parabola y^2=4x have maximum num...

    Text Solution

    |

  5. The slope of line which belongs to family (1+ l) x + (l-1)y + 2(1-l) =...

    Text Solution

    |

  6. If 3x+4y+k=0 represents the equation of tangent at the vertex of the ...

    Text Solution

    |

  7. Normals at (x(1),y(1)),(x(2),y(2))and(x(3),y(3)) to the parabola y^(2)...

    Text Solution

    |

  8. Foot of perpendicular from point P on the parabola y^(2)=4ax to the ax...

    Text Solution

    |

  9. Find the integrating factor of the following differential equation: x...

    Text Solution

    |

  10. Normals are drawn from a point P with slopes m1,m2 and m3 are drawn fr...

    Text Solution

    |

  11. The curve be y=x^2 whose slopeof tangent is x, so find the point of in...

    Text Solution

    |

  12. Find the point of intersection of the curves y= 2x^2-x+1 and y=3x+4 wh...

    Text Solution

    |

  13. Find the principal value of cos^(-1) (-(sqrt3)/2)

    Text Solution

    |

  14. If the normals of the parabola y^2=4x drawn at the end points of its l...

    Text Solution

    |

  15. If the length of the latus rectum rectum of the parabola 169{(x-1)^(2)...

    Text Solution

    |

  16. If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b),...

    Text Solution

    |

  17. Consider the locus of center of the circle which touches the circle x^...

    Text Solution

    |

  18. Line y=2x-b cuts the parabola y=x^(2)-4x at points A and B. Then the v...

    Text Solution

    |

  19. A line through the origin intersects the parabola 5y=2x^(2)-9x+10 at t...

    Text Solution

    |

  20. If 3x+4y+k=0 represents the equation of tangent at the vertex of the ...

    Text Solution

    |