Home
Class 12
MATHS
If the straight line lx+my=1 touches th ...

If the straight line `lx+my=1` touches th curve `(ax)^(n)+(by)^(n)=1`. Then show that,
`((l)/(a))^((n)/(n-1))+((m)/(b))^((n)/(n-1))=1`.

Promotional Banner

Topper's Solved these Questions

  • TANGENT AND NORMAL

    CHHAYA PUBLICATION|Exercise A MULTIPLE CORRECT ANSWER TYPE|5 Videos

  • TANGENT AND NORMAL

    CHHAYA PUBLICATION|Exercise INTEGER ANSWER TYPE|5 Videos

  • TANGENT AND NORMAL

    CHHAYA PUBLICATION|Exercise SHORT ANSWER TYPE QUESTIONS|42 Videos

  • STRAIGHT LINE IN THREE DIMENSINAL SPACE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination|19 Videos

  • TRANSFORMATIONS OF SUMS AND PRODUCTS

    CHHAYA PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

If the straight line (x)/(h)+(y)/(k)=1 touches the curve (x/a)^(n)+((y)/(b))^(n)=1 , then show that ((a)/(h))^((n)/(n-1))+((b)/(k))^((n)/(n-1))=1

If the straight line lx+my+n=0 touches the : circle x^(2)+y^(2)=a^(2) , show that a^(2)(l^(2)+m^(2))=n^(2)

If the straight line lx+my+n=0 touches the : parabola y^(2)=4ax , prove that am^(2)=nl

If the straight line lx+my+n=0 touches the : hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , show that a^(2) l^(2)-b^(2)m^(2)=n^(2) .

If the straight line lx+my=n is a normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 show that (a^(2))/(l^(2))-(b^(2))/(m^(2))=((a^(2)+b^(2))^(2))/(n^(2)) .

Show that log_(b)(1/(b^n)) = -n

Show that , .^(n)P_(r)=n.^(n-1)P_(r-1)=(n-r+1).^(n)P_(r-1) .

Find the condition that the straight line lx+my=n touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

Show : 2^(n)-(n)/(1!).2^(n-1)+(n(n-1))/(2!).2^(n-2)-....+(-1)^(n)=1

Show that ("lim")_(n vec oo)(1/(n+1)+1/(n+2)++1/(6n))=log6

CHHAYA PUBLICATION-TANGENT AND NORMAL -LONG ANSWER TYPE QUESTIONS
  1. Find the condition that the straight line x cos alpha+ y sin alpha=p i...

    Text Solution

    |

  2. hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1.

    Text Solution

    |

  3. If the straight line lx+my=1 touches th curve (ax)^(n)+(by)^(n)=1. The...

    Text Solution

    |

  4. If the straigjht line x cos alpha+ y sin alpha=p touches the curve x^(...

    Text Solution

    |

  5. Show that the tangents at the ends of latus rectum of an ellipse inter...

    Text Solution

    |

  6. Find the equation of the common tangent to the circle x^(2)+y^(2)=8 an...

    Text Solution

    |

  7. Find the equation o of the common tangent to the parabolas y^(2)=32x ...

    Text Solution

    |

  8. Find the common tangents to the hyperbola x^(2)-2y^(2)=4 and the circl...

    Text Solution

    |

  9. The equation of the tangent to the curve y^(2)=ax^(3)+b at the point (...

    Text Solution

    |

  10. In each of the following cases find the angle between the given curves...

    Text Solution

    |

  11. In each of the following cases find the angle between the given curves...

    Text Solution

    |

  12. Show that curves x^(3)-3xy^(2)+2=0 and y^(3)-3x^(2)y+2=0 intersect at ...

    Text Solution

    |

  13. If the curves ax^(2)+by^(2)=1 and cx^(2)+dy^(2)=1 intersect at right a...

    Text Solution

    |

  14. The equation of the tangent to the curve y=a+bx+cx^() where it meet th...

    Text Solution

    |

  15. If x(1) and y(1) be the intercepts on the x and y-axis respectively of...

    Text Solution

    |

  16. Show that the length of the portion of the tangent to the curve x^((2)...

    Text Solution

    |

  17. Show that the sum of the intercept on the coordinates axes of tangent ...

    Text Solution

    |

  18. If h and k be the intercept on the coordinates axes of tangent to the ...

    Text Solution

    |

  19. Find the equation of the normal to the parabola y^(2)=4ax at a point (...

    Text Solution

    |

  20. Find the coodition that the straight line lx+my+n=0 is a normal to the...

    Text Solution

    |