Home
Class 11
MATHS
Through the point P(alpha,beta) , where ...

Through the point `P(alpha,beta)` , where `alphabeta>0,` the straight line `x/a+y/b=1` is drawn so as to form a triangle of area `S` with the axes. If `a b >0,` then the least value of `S` is

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If the straight lines 2x+3y-1=0,x+2y-1=0,and ax+by-1=0 form a triangle with the origin as orthocentre, then (a , b) is given by

If a pair of perpendicular straight lines drawn through the origin forms an isosceles triangle with the line 2x+3y=6 , then area of the triangle so formed is

A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is-

A line is drawn through the point ( 1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

Find the area of the triangle formed by the straight line x sin alpha + y cos alpha = p with the axes of coordinates .

A straight line passes through the point (2,3) and forms a triangle of area 12 square unit with the coordinate axes . Find the equation of the straight line .

A pair of perpendicular straight lines drawn through the origin from an isosceles triangle with line 2x+3y=6, then area of the triangle so formed is

Find the equation of the straight line which parallel with 3x+2y-6=0 and forms a triangle of area 21 square units with the straight lines x-2y=0 and y-2x=0.

If the straight line 2x-3y+17=0 is perpendicular to the line passing through the points (7, 17) and (15, beta) , then beta equals

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. If (-4,0) and (1,-1) are two vertices of a triangle of area 4s qdotu n...

    Text Solution

    |

  2. Let 0-=(0,0),A-=(0,4),B-=(6,0)dot Let P be a moving point such that th...

    Text Solution

    |

  3. Through the point P(alpha,beta) , where alphabeta>0, the straight line...

    Text Solution

    |

  4. The vertices A and D of square A B C D lie on the positive sides of x-...

    Text Solution

    |

  5. A light ray emerging from the point source placed at P(2,3) is reflect...

    Text Solution

    |

  6. If the origin is shifted to the point ((a b)/(a-b),0) without rotation...

    Text Solution

    |

  7. In Delta ABC, the coordinates of B are (0,0) AB=2,angleABC=pi//3, and ...

    Text Solution

    |

  8. If in triangle ABC, A=(1, 10), circumcentre=(-1/3, 2/3) and orthocentr...

    Text Solution

    |

  9. Find The orthocenter of the triangle formed by (0,0),(8,0),(4,6)

    Text Solution

    |

  10. In A B C , if the orthocentre is (1,2) and the circumcenter is (0, 0)...

    Text Solution

    |

  11. If the vertices of a triangle are (sqrt(5,)0) , (sqrt(3),sqrt(2)) , an...

    Text Solution

    |

  12. The vertices of a triangle are (p q ,1/(p q)),(q r ,1/(q r)), and (r p...

    Text Solution

    |

  13. If two vertices of a triangle are (-2,3) and (5,-1) the orthocentre li...

    Text Solution

    |

  14. P and Q are points on the line joining A(-2,5) and B(3,1) such that AP...

    Text Solution

    |

  15. The point (4,1) undergoes the following three transformations successi...

    Text Solution

    |

  16. If the coordinates of the vertices of a triangle are rational numbers,...

    Text Solution

    |

  17. If P(1,2) ,Q(4,6),R(5,7), and S(a , b) are the vertices of a parallelo...

    Text Solution

    |

  18. If the area of the triangle formed by the points (2a ,b)(a+b ,2b+a), a...

    Text Solution

    |

  19. The incenter of the triangle with vertices (1,sqrt(3)),(0,0), and (2,...

    Text Solution

    |

  20. The locus of the moving point whose coordinates are given by (e^t+e^(-...

    Text Solution

    |