Home
Class 11
MATHS
If P(alpha,beta) is a point on the ell...

If `P(alpha,beta)` is a point on the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` with foci `S a n d S '` and eccentricity `e ,` then prove that the area of Δ` S P S '` is `be sqrt(a^2-alpha^2)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If P is a point on the ellipse (x^(2))/16+(y^(2))/25=1 whose foci are S and S', then PS+PS'=8.

P is any point on the ellipise (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and S and S' are its foci, then maximum value of the angle SPS' is

If P is a point on the ellipse (X^(2))/(9) + (y^(2))/(4) =1 whose foci are S and S' then the value of PS + PS' is

Let P be a variable point on the ellipse (x^(2))/(25)+(y^(2))/(16)=1 with foci at S and S'. Then find the maximum area of the triangle SPS'

If P is any point lying on the ellipse x^2/a^2+y^2/b^2=1 , whose foci are S and S' . Let /_PSS'=alpha and /_PS'S=beta ,then

If P is a point on the ellipse (x^(2))/(36)+(y^(2))/(9)=1 , S and S ’ are the foci of the ellipse then find SP + S^1P

Let P be a variable point on the ellipse x^(2)/25 + y^(2)/16 = 1 with foci at S and S'. If A be the area of triangle PSS' then the maximum value of A, is

Let P be a variable point on the ellipse x^(2)/25 + y^(2)/16 = 1 with foci at S and S'. If A be the area of triangle PSS' then the maximum value of A, is

If P is any point on the ellipse 9x^(2) + 36y^(2) = 324 whose foci are S and S'. Then, SP + S' P equals

P is any point lying on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(agtb) whose foci are S and S'. If anglePSS'=alpha and anglePS'S=beta , then the value of tan.(alpha)/(2)tan.(beta)/(2) is

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the foci of the ellipse 25(x+1)^2+9(y+2)^2=225.

    Text Solution

    |

  2. Find the equation of an ellipse whose axes are the x-and y-axis and...

    Text Solution

    |

  3. If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1...

    Text Solution

    |

  4. An arc of a bridge is semi-elliptical with the major axis horizonta...

    Text Solution

    |

  5. An ellipse has O B as the semi-minor axis, F and F ' as its foci, ...

    Text Solution

    |

  6. P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with AA ' ...

    Text Solution

    |

  7. Prove that the curve represented by x=3(cost+sint),y=4(cost-sint),t in...

    Text Solution

    |

  8. Find the center, foci, the length of the axes, and the eccentricity...

    Text Solution

    |

  9. If C is the center and A ,B are two points on the conic 4x^2+9y^...

    Text Solution

    |

  10. Find the equation of a chord of the ellipse (x^2)/(25)+(y^2)/(16)=1 jo...

    Text Solution

    |

  11. Prove that the chords of contact of pairs of perpendicular tangents to...

    Text Solution

    |

  12. Tangent are drawn from the point (3, 2) to the ellipse x^2+4y^2=9 ....

    Text Solution

    |

  13. Find the locus of the point of intersection of tangents to the elli...

    Text Solution

    |

  14. Tangents are drawn from the points on the line x-y-5=0 to x^2+4y^2=4 ....

    Text Solution

    |

  15. If from a point P , tangents PQ and PR are drawn to the ellipse (x^2...

    Text Solution

    |

  16. Prove that the chord of contact of the ellipse (x^2)/(a^2)+(y^2)/(b^2)...

    Text Solution

    |

  17. The locus a point P(alpha,beta) moving under the condition that the li...

    Text Solution

    |

  18. Find the locus of the point which is such that the chord of contact...

    Text Solution

    |

  19. A point P moves such that the chord of contact of the pair of tangents...

    Text Solution

    |

  20. Find the length of the chord of the ellipse x^2/25+y^2/16=1, whose mid...

    Text Solution

    |