Home
Class 12
MATHS
Find the condition that the straight lin...

Find the condition that the straight line `x cos alpha+ y sin alpha=p` is a tangent to the :
ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`

Text Solution

Verified by Experts

The correct Answer is:
`a^(2) cos^(2) alpha+b^(2) sin^(2) alpha= p^(2)`
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 y= x sin alpha + a sec alpha is a tangent to the circle x^(2) + y^(2) = a^(2) then-

Show that the straight line x cosalpha+y sin alpha=p is a tangent to the curve (x^(m))/(a^(m))+(y^(m))/(b^(m))=1 , if (a cos alpha)^((m)/(m-1))+(b sin alpha)^((m)/(m-1))=p^((m)/(m-1))

The locus of a point P ( alpha , beta ) moving under the condition that the line y= alpha x + beta is a tangent to the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2))=1 is a/an-

Find the condition that the straight line x cos theta+ y sin theta =p may touch the parabola y^(2)= 4ax .

Find the coodition that the straight line lx+my+n=0 is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

The straight line x + y = a will be a tangent to the ellipse (x^(2))/(9) + (y^(2))/(16) = 1 if the value of a is -

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

If the straight line y= x sin alpha+ a sec alpha be a tangent ot the circle x^(2)+y^(2)=a^(2) , then show that cos^(2)alpha=1

If x cos alpha +y sin alpha = 4 is tangent to (x^(2))/(25) +(y^(2))/(9) =1 , then the value of alpha is

The angle made by the straight line x cos alpha + y sin alpha = p with the negative direction of x - axis is _

CHHAYA PUBLICATION-TANGENT AND NORMAL -LONG ANSWER TYPE QUESTIONS
  1. If the straight line y= x sin alpha+ a sec alpha be a tangent ot the c...

    Text Solution

    |

  2. Find the condition that the straight line x cos theta+ y sin theta =p ...

    Text Solution

    |

  3. Find the condition that the straight line x cos alpha+ y sin alpha=p i...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |