Home
Class 12
MATHS
If (alpha +beta ) and (alpha - beta )...

If `(alpha +beta )` and `(alpha - beta )` are the eccentric angles of the points P and Q respectively on the ellipse `(x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 ` show that the equation of the chord PQ is `(x)/(a) cos alpha+(y)/(b)sin alpha = cos beta . `

Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CHHAYA PUBLICATION|Exercise Short Answer Type Questios|48 Videos
  • ELLIPSE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams ( A M . C . Q )|5 Videos
  • ELLIPSE

    CHHAYA PUBLICATION|Exercise M . C . Q|20 Videos
  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos
  • GENERAL SOLUTIONS OF TRIGNOMETRIC EQUATIONS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type-|2 Videos

Similar Questions

Explore conceptually related problems

If (alpha+beta) and (alpha-beta) are the eccentric angles of the points P and Q respectively on the ellipse x^2/25+y^2/9=1 .Show that the equation of the chord PQ is x/5cosalpha+y/3sinalpha=cosbeta

P( asec alpha, b tan alpha ) and Q (a sec beta, b tan beta) are two given points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1. Show that the equation of the chord PQ is (x)/(a) cos (alpha - beta)/(2) - (y)/(b) sin (alpha + beta)/(2) = cos (alpha+beta)/(2).

If the eccentric angles of the any two points P,Q on the ellipse x^2/a^2+y^2/b^2=1 are (alpha+beta) and (alpha-beta) resp.Show that the equation of chord PQ is x/a cosalpha+y/b sinalpha=cosbeta

If sin alpha + sin beta = p "and" cos alpha + cos beta = q "then the value of " "tan" (alpha-beta)/2 will be-

sin alpha + sin beta = a "and" cos alpha + cos beta = b cos (alpha + beta) =

sin alpha + sin beta = a "and" cos alpha + cos beta = b sin (alpha + beta) =

In sin alpha+ sin beta=(1)/(2) and cos alpha+ cos beta =(5)/(4) , find the value of tan alpha+tan beta .

If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 subtends a right angle at the vertex A(a ,0), then prove that tan(alpha/2)tan(beta/2)=-(b^2)/(a^2)dot

If alpha and beta be the eccentric angles of the extremities of a focal chord of the hyperbola b^(2)x^(2) - a^(2)y^(2) = a^(2)b^(2) , show that, tan(alpha)/(2)tan(beta)/(2) = -(e-1)/(e+1) , (e-1)/(e+1) (e is the eccentricity of the hyperbola.).

CHHAYA PUBLICATION-ELLIPSE-Very Short Answer Type Qustions
  1. Find the coordinates of a point on the ellipse x^(2) + 2y^(2) = 4 ...

    Text Solution

    |

  2. If the ellipse (x^(2))/(a(1)^(2))+(y^(2))/(b(1)^(2))=1(a(1)^(2)gtb(1)^...

    Text Solution

    |

  3. Find (i) the centre, (ii) vertices, (iii) equations of the axes, (iv) ...

    Text Solution

    |

  4. Find (i) the centre, (ii) vertices, (iii) equations of the axes, (iv) ...

    Text Solution

    |

  5. Find (i) the centre, (ii) vertices, (iii) equations of the axes, (iv) ...

    Text Solution

    |

  6. Find the eccentricity, the length of latus rectum and the centre of e...

    Text Solution

    |

  7. Find the latus rectum , eccentricity and the coordinates of the foci o...

    Text Solution

    |

  8. Examine, with reasons, the validity of the following statement : x^(2...

    Text Solution

    |

  9. The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through (-3 , ...

    Text Solution

    |

  10. The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through the...

    Text Solution

    |

  11. The coordinates of the centre and of a vertex of an ellipse are (-2,-...

    Text Solution

    |

  12. The vertices of an ellipse are (-1,2) and (9,2) . If the eccentrici...

    Text Solution

    |

  13. Find the equation of the ellipse whose foci are (2,3) and (-2,3) an...

    Text Solution

    |

  14. The eccentricity of an ellipse is (2)/(3) and the coordinates of its ...

    Text Solution

    |

  15. The distance of a point of the ellipse x^(2) + 3y^(2) = 6 from its ...

    Text Solution

    |

  16. PQ is any double ordinate of the ellipse (x^(2))/(a^(2))+(y^(2))/(b...

    Text Solution

    |

  17. Show that the double ordinate of the auxiliary circle of an ellipse pa...

    Text Solution

    |

  18. O is the centre of an ellipse whose semi-minor axis is b . The ordina...

    Text Solution

    |

  19. If (alpha +beta ) and (alpha - beta ) are the eccentric angles ...

    Text Solution

    |

  20. If the theta and varphi be the eccentric angles of the two ends o...

    Text Solution

    |