Home
Class 11
MATHS
A straight line through the origin O mee...

A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y+ 6=0 at points P and Q respectively. Then the point O divides the segment PQ in the ratio :

A

`1:2`

B

`3:4`

C

`2:1`

D

` 4: 3`.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise EXERCISE|478 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

  • INFINITE SERIES

    MODERN PUBLICATION|Exercise EXAMPLE|10 Videos

Similar Questions

Explore conceptually related problems

A straight line L through the origin meets the lines x + y = 1 and x + y = 3 at P and Q respectively. Through P and Q two Straight lines L_1 and L_2 are drawn parallel to 2x- y=5 and 3x+y=5 respectively. Lines L_1 and L_2 intersect at R. Show that the locus of R, as L varies, is a straight line.

A straight line through the point (2, 2) intersects the lines sqrt3x + y = 0 and sqrt3 x-y=0 at the points A and B. The equation to the line AB so that the triangle OAB is equilateral is ,

A variable line L drawn through O(0,0) to meet line l1: y-x-10=0 and L2:y-x-20=0 at the point A and B respectively then locus of point p is ' such that (OP)^(2) = OA . OB,

P and Q are two points with position vectors 2veca+2vecb and veca +vecb respectively. Write the position vector of a point R, which divides the line segment PQ in the ratio 2 : 1 externally.

Find the equation of the straight line, which passes through the point (1, 4) and is such that the segment of the line intercepted between the axes is divided by the point in the ratio 1: 2.

Find the point of intersection of the straight lines : 2x + 3y-6 = 0, 3x - 2y-6= 0 .

P and Q are two points with position vectors 3veca-3vecb and veca+vecb respectively. Write the position vector of a point R which divides the line segment PQ in the ratio 2 : 1 externally.

Find equation of the line which is equidistant from parallel lines 9x + 6y -7 = 0 and 3x + 2y+6 = 0 .

A line through the origin meets the circle x^(2)+y^(2)=a^(2) at P and the hyperbola x^(2)-y^(2)=a^(2) at Q. Prove that the locus of the point of intersection of tangent at P to the circle with the tangent at Q to the hyperbola is a straight line.

A straight line through A (-15 -10) meets the lines x-y-1=0 , x+2y=5 and x+3y=7 respectively at A, B and C. If 12/(AB)+40/(AC)=52/(AD) prove that the line passes through the origin.

MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. The equation of the common tangent to the curves , y^2=8x and xy=-1 is...

    Text Solution

    |

  2. If the tangent at the point P on the circle x^2+y^2+6x + 6y = 2 meets ...

    Text Solution

    |

  3. A straight line through the origin O meets the parallel lines 4x + 2y ...

    Text Solution

    |

  4. Let P=(-1,0) ,Q =(0,0) and R (3,3sqrt(3)) be three point . The equatio...

    Text Solution

    |

  5. Let 0ltalphalt(pi)/(2) be a fixed angle. If P=(costheta,sintheta)andQ=...

    Text Solution

    |

  6. A triangle with vertices (2, 0), (- 1,- 1),(1,0) is :

    Text Solution

    |

  7. The straight lines 2x+11y - 5 = 0 , 24 x + 7y - 20 = 0 and 4x - 3y - ...

    Text Solution

    |

  8. A straight line through the point (2, 2) intersects the lines sqrt3x +...

    Text Solution

    |

  9. Find the incentre of the triangle with vertices A(1,sqrt3), B(0,0) and...

    Text Solution

    |

  10. The equation of the tangent to the circle x^2 + y^2+4x- 4y + 4 =0, whi...

    Text Solution

    |

  11. Find the area bounded by the ellipse x^(2)/16+y^(2)/9=1

    Text Solution

    |

  12. The equation of the chord joining two points (x1, y1) and (x2, y2) on ...

    Text Solution

    |

  13. A square of side a lies above the X- axis and has one vertex at the or...

    Text Solution

    |

  14. Find the slope of the tangent to the curve y=3x^4−4 at x = 4

    Text Solution

    |

  15. The lines 2x-3y=5 and 3x-4y=7 are the diameters of a circle of area 15...

    Text Solution

    |

  16. If the two circles (x-1)^2+(y-3)^2= r^2 and x^2+y^2-8x+2y+8=0 interse...

    Text Solution

    |

  17. The normal at the point (bt1^2, 2bt1) on a parabola meets the parabola...

    Text Solution

    |

  18. If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola ...

    Text Solution

    |

  19. The orthocentre of the triangle with vertices (0,0),(3,4), and (4,0) i...

    Text Solution

    |

  20. A square is formed by following two pairs of straight lines : y^2 -14...

    Text Solution

    |