Home
Class 12
MATHS
If P divides O A internally in the ra...

If `P` divides `O A` internally in the ratio `lambda_1:lambda_2` and `Q` divides `O A` externally in the ratio `lambda_1;lambda_2,` then prove that `O A` is the harmonic mean of `O P` and `O Qdot`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CENGAGE PUBLICATION|Exercise All Questions|238 Videos

Similar Questions

Explore conceptually related problems

If point P(3,2) divides the line segment AB internally in the ratio of 3:2 and point Q(-2,3) divides AB externally in the ratio 4:3 then find the coordinates of points A and B.

If the point (lambda,1+lambda) be lying inside the circle x^2+y^2 =1 then

Let P\ a n d\ Q be any two points. Find the coordinates of the point R\ which divides P Q externally in the ratio 2:1 and verify that Q is the mid point of P R .

Let O be the vertex and Q be any point on the parabola x^2=8y . IF the point P divides the line segment OQ internally in the ratio 1:3 , then the locus of P is

Point P divides line joining A(-5,1) and B(3,5) in the ratio lambda:1 . The coordinates of P and Q are (1,5) and (7,2) respectively . If the area of the triangle PQR be 2 sq . Units , then the value of lambda is -

Wavelengths of visible light, X-rays and infrared rays are lambda_1,lambda_2 and lambda_3 , respectively. Arrange them in ascending order of their magnitudes.

The equation (x^(2))/(9-lambda)+(y^(2))/(4-lambda) =1 represents a hyperbola when a lt lambda lt b then (b-a)=

If (lambda, 1+lambda) be lying inside the circle x^(2)+y^(2)=1 , then-

Find the co-ordinates of the point which divided the join of P(5,-2) and Q(9,6). externally in ratio 3:1

Let O be the vertex and Q be any point on the parabola x^(2) = 8 y . If the point P divides the line segments OQ internally in the ratio 1 : 3 , then the locus of P is _

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. If the points (1,1):(0,sec^2theta); and (cos e c^2theta,0) are coll...

    Text Solution

    |

  2. Given that A1,A2,A3, An are n points in a plane whose coordinates ...

    Text Solution

    |

  3. If P divides O A internally in the ratio lambda1:lambda2 and Q divi...

    Text Solution

    |

  4. Prove that the point (-2,-1),(1,0),(4,3)a n d(1,2) are the vertices of...

    Text Solution

    |

  5. Determine the ratio in which the line 3x+y-9=0 divides the segment ...

    Text Solution

    |

  6. Find the orthocentre of the triangle whose vertices are (0,0),(3,0)...

    Text Solution

    |

  7. If a vertex of a triangle is (1,1) , and the middle points of two side...

    Text Solution

    |

  8. The vertices of a triangle are A(-1,-7),B(5,1)a n dC(1,4)dot If the ...

    Text Solution

    |

  9. If A B C having vertices A(acostheta1,asintheta1),B(acostheta2asin...

    Text Solution

    |

  10. If the point (x ,-1),(3, y),(-2,3),a n d(-3,-2) taken in order are ...

    Text Solution

    |

  11. If the midpoints of the sides of a triangle are (2,1),(-1,-3),a n d(4,...

    Text Solution

    |

  12. If the circumcenter of an acute-angled triangle lies at the origin ...

    Text Solution

    |

  13. If a vertex, the circumcenter, and the centroid of a triangle are (0...

    Text Solution

    |

  14. Orthocenter and circumcenter of a Delta A B C are (a , b)a n d(c , d) ...

    Text Solution

    |

  15. If A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of traingle ABC and...

    Text Solution

    |

  16. The points (a , b),(c , d), and ((k c+l a)/(k+l),(k d+l b)/(k+l)) are ...

    Text Solution

    |

  17. The circumcenter of the triangle formed by the line y=x ,y=2x , and ...

    Text Solution

    |

  18. The line joining A (b cos alpha, b sin alpha ) and B (a cos beta, a si...

    Text Solution

    |

  19. If the middle points of the sides of a triangle are (-2,3),(4,-3),a...

    Text Solution

    |

  20. In what ratio does x-axis divide the line segment joining (2, -3) and ...

    Text Solution

    |