Home
Class 12
MATHS
A vertical line passing through the p...

A vertical line passing through the point (h,0) intersects the ellipse `(x^(2))/(4)+(y^(2))/(3)=1` at the points P and Q.
Let the tangents to the ellipse at P and Q meet at the point R. if `Delta(h) =` area of the triangle `PQR , Delta,= underset(1//2 le h le1)("max") Delta (h) " and "Delta_(2) = underset(1//2 le h le 1)("min") Delta(h) , " then "(8)/(sqrt(5)) Delta_(1) -8Delta_(2)=`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-3 Part II|22 Videos
  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise High Level Problems (HLP)|33 Videos
  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-2 Part IV comprehension|11 Videos
  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

Similar Questions

Explore conceptually related problems

A vertical line passing through the point (h,0) intersects the ellipse (x^(2))/(4)+(y^(2))/(3)=1 at the points P and Q. Let the tangents to the ellipse at P and Q meet at R. If delta(h) Area of triangle delta PQR, and delta_(1)max_((1)/(2)<=h<=1)delta(h) A further delta_(2)min_((1)/(2)<=h<=1)delta(h) Then (8)/(sqrt(5))delta_(1)-8 delta_(2)

Lines x+y=1 and 3y=x+3 intersect the ellipse x^(2)+9y^(2)=9 at the points P,Q,R. the area of the triangles PQR is

The straight line (x)/(4)+(y)/(3)=1 intersects the ellipse (x^(2))/(16)+(y^(2))/(9)=1 at two points A and B such that area of Delta PAB is equal to 3, the number of such P's is/are

The straight line (x)/(4)+(y)/(3)=1 intersects the ellipse (x^(2))/(16)+(y^(2))/(9)=1 at two points A and B there is a point P on this ellipse such that the area of Delta PAB is equal to 6(sqrt(2)-1) .Then the number of such point (P) is/are

Tangents are drawn from the point P(3, 4) to the ellipse x^2/9 +y^2/4 =1 touching the ellipse at points A and B. The orthocenter of the triangle PAB is

The line x+2y=1 cuts the ellipse x^(2)+4y^(2)=1 1 at two distinct points A and B. Point C is on the ellipse such that area of triangle ABC is maximum, then find point C.

The straight line (x)/(4)+(y)/(3)=1 intersects the ellipse (x^(2))/(16)+(y^(2))/(9)=1 at two points A and B there is a point P on this ellipse such that the area of Delta PAB is equal to 6(sqrt(2)-1) . Then the number of such point (P) is/are (A) 4 (B) 1 (C) 2 (D) 3

RESONANCE-APPLICATION OF DERIVATIVES-Exersise-3 Part I
  1. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  2. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is 6 (b)...

    Text Solution

    |

  3. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  4. A vertical line passing through the point (h,0) intersects the ell...

    Text Solution

    |

  5. The function f(x)=2|x|+|x+2|=||x|2|-2|x|| has a local minimum or a loc...

    Text Solution

    |

  6. Let f[0, 1] -> R (the set of all real numbers be a function.Suppose t...

    Text Solution

    |

  7. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  8. line L:y=mx+3 meets y–axis at E(0, 3) and the are of the parabola y^(2...

    Text Solution

    |

  9. Let a in R and let f: R to R be given by f(x) =x^(5) -5x+a. then

    Text Solution

    |

  10. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

    Text Solution

    |

  11. A cylindrica container is to be made from certain solid material with ...

    Text Solution

    |

  12. Let f,g:[-1,2]rarr RR be continuous functions which are twice differen...

    Text Solution

    |

  13. Let f: R to (0 ,oo)" and " g :R to R be twice differentiable function...

    Text Solution

    |

  14. Which of the following options is the only INCORRECT combination ?

    Text Solution

    |

  15. Which of the following options is the only CORRECT combination

    Text Solution

    |

  16. Which of the following options is the only CORRECT combination ?

    Text Solution

    |

  17. If f:R->R is a twice differentiable function such that f''(x) > 0 for ...

    Text Solution

    |

  18. If f:RR-> RR is a differentiable function such that f(x) > 2f(x) f...

    Text Solution

    |

  19. then

    Text Solution

    |

  20. For every twice differentiable function f: R->[-2,\ 2] with (f(0))^...

    Text Solution

    |