Home
Class 12
MATHS
Show that the line xcosalpha+y sinalpha+...

Show that the line `xcosalpha+y sinalpha+p` touches the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1` if `a^(2)cos^(2)alpha=b^(2)sin^(2)alpha=p^(2)` and the point of contact is `(a^(2)cosalpha/p),(b^(2)sinalpha/p)`.

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

If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^2)-(y^2)/(b^2)=1, then prove that a^2cos^2alpha-b^2sin^2alpha=p^2dot

The line x cos alpha + y sin alpha = p is tangent to the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) = 1 if :

Show that xcosalpha+asin^2alpha=p touches the parabola y^2=4a x if pcosalpha+asin^2alpha=0 and that the point of contact is (atan^2alpha,-2atanalpha)dot

If x/a+y/b=sqrt(2) touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentric angle theta of point of contact.

Find the condition that the line x cos alpha+y sin alpha=p may touch the curve ((x)/(a))^(m)+((y)/(b))^(m)=1

Show that the tangents at the ends of conjugate diameters of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 intersect on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=2 .

Find the condition that the line x cos alpha + y sin alpha = p may be a tangent to the curve (x^2)/(a^2) + (y^2)/(b^2) = 1

MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Show that the line xcosalpha+y sinalpha+p touches the ellipse x^(2)/a^...

    Text Solution

    |

  2. Find the rate of change of the area of a circle with respect to its ra...

    Text Solution

    |

  3. Find the rate of change of the area of a circle with respect to its ra...

    Text Solution

    |

  4. An edge of a variable cube is increasing at the rate of 3 cm/s. How fa...

    Text Solution

    |

  5. The radius of a soap-bubble is increasing at the rate of 0.2cm/s. Find...

    Text Solution

    |

  6. The radius of a circle is increasing at the rate of 0.7 cm/s. What is ...

    Text Solution

    |

  7. The radius of a circle is increasing uniformly at the rate of 4 cm per...

    Text Solution

    |

  8. If the area of a circle increases uniformly, then show that the rate o...

    Text Solution

    |

  9. The radius of a circle is increasing uniformly at the rate of 3 cm/s. ...

    Text Solution

    |

  10. The radius of an air bubble is increasing at the rate of 1/2 cm/s. At...

    Text Solution

    |

  11. The radius of spherical balloon is increasing at the rate 5 cm per sec...

    Text Solution

    |

  12. The radius of a spherical soap bubble is increasing at the rate of 0.3...

    Text Solution

    |

  13. A balloon, which always remains spherical, has a variable diameter 3/2...

    Text Solution

    |

  14. A balloon, which always remains spherical on inflation, is being infla...

    Text Solution

    |

  15. The volume of a cube is increasing at the rate of 9 "cm"^(3)//sec. How...

    Text Solution

    |

  16. The volume of a cube is increasing at the rate of 8 cm^3/s. How fast i...

    Text Solution

    |

  17. The volume of a cube is increasing at the rate of 7 cubic metre per se...

    Text Solution

    |

  18. A particle moves along the curve y=4/(3)x^(3)+5. Find the points on th...

    Text Solution

    |

  19. A particle move along the curve 6y = x^3 +2. Find the points on the cr...

    Text Solution

    |

  20. The radius of a cylinder increases at the rate of 1 cm/s and its heigh...

    Text Solution

    |

  21. The contentment obtained after eating X-units of a new dish at a trial...

    Text Solution

    |