Home
Class 12
MATHS
If the curves: alphax^2 + betay^2 =1 and...

If the curves: `alphax^2 + betay^2 =1 and alpha'x^2 + beta'y^2=1` intersect orthogonally, prove that `(alpha-alpha') betabeta' = (beta-beta') alphaalpha'`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    MODERN PUBLICATION|Exercise EXERCISE|433 Videos

  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise EXERCISE|211 Videos

Similar Questions

Explore conceptually related problems

Using vectors, prove that sin (alpha+beta)=sin alpha cos beta+ cos alpha sin beta .

Using vectors prove that sin(alpha - beta) = sin alpha cos beta- cos alpha sin beta .

If (cos^4 alpha)/(cos^2 beta)+ (sin^4 alpha)/(sin^2 beta) =1 , prove that : sin^4 alpha+ sin^4 beta= 2 sin^2 alpha sin^2 beta .

If 2 tan beta+cot beta= tan alpha , prove that cot beta= 2 tan (alpha-beta) .

If a tan alpha+b tan beta=(a+b) tan ((alpha+beta)/2) , where alpha ne beta , prove that : a cos beta= b cos alpha .

If cos (alpha+beta)=4/5, sin (alpha -beta)=5/13 and alpha, beta lie between 0 and pi/4 , prove that tan 2 alpha = 56/33 .

Let -pi/6 beta_1 and alpha_2 >beta_2 , then alpha_1 + beta_2 equals:

If tan alpha= n tan beta and sin alpha= m sin beta , prove that cos^2 alpha= (m^2-1)/(n^2-1) .

If (cos^4 alpha)/(cos^2 beta)+ (sin^4 alpha)/(sin^2 beta) =1 , prove that : (cos^4 beta)/(cos^2 alpha)+ (sin^4 beta)/ (sin^2 alpha) =1 .

If alpha and beta satisfying 2 sec2 alpha = tan beta + cot beta , then alpha+beta =

MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Show that the following curves cut each other orthogonally: y = x^3 an...

    Text Solution

    |

  2. Show that the following curves cut each other orthogonally: x^2 + 4y^2...

    Text Solution

    |

  3. If the curves: alphax^2 + betay^2 =1 and alpha'x^2 + beta'y^2=1 inters...

    Text Solution

    |

  4. Prove that the curves 4x = y^2 and 4xy = k cut at right angles if k^2...

    Text Solution

    |

  5. Show that the curves 2x = y^2 and 2xy = k cut at right angles if k^2 =...

    Text Solution

    |

  6. Prove that the curves y^(2)=4axandxy=c^(2) cut at right angles if c^(4...

    Text Solution

    |

  7. Show that the normal at any point theta to the curve x = a cos theta +...

    Text Solution

    |

  8. Find the equations of the tangent and normal to the curve 16x^2 + 9y^2...

    Text Solution

    |

  9. Find a point on the curve y=x^(3), where the tangent to the curve is p...

    Text Solution

    |

  10. Find a point on the parabola y =(x-3)^2, where the tangent is parallel...

    Text Solution

    |

  11. Show that the area of the triangle formed by the tangent and the norma...

    Text Solution

    |

  12. Find the equations of the normal at a point on the curve x^2=4y, which...

    Text Solution

    |

  13. Find the equations of the tangents to the curve 3x^2 - y^2 = 8, which ...

    Text Solution

    |

  14. Determine the values of 'x' for which the function f(x) = x^2 + 2x - 3...

    Text Solution

    |

  15. Determine the intervals in which the function f(x) = (x-1)(x+1)^2 is i...

    Text Solution

    |

  16. Using differentials, find the approximate value of sqrt26

    Text Solution

    |

  17. Using differentials, find the approximate the value of root3(0.026) up...

    Text Solution

    |

  18. Find the approximate change in the volume V of a cube of side x metres...

    Text Solution

    |

  19. If the radius of a sphere is measured as 9 m with an error of 0.03 m, ...

    Text Solution

    |

  20. If y = x^4 + 10 and x changes from 2 to 1.99, find the approximate cha...

    Text Solution

    |