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

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

Text Solution

Verified by Experts

The correct Answer is:
`a sin^(2) alpha+ p cos alpha=0`
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

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

The line, among the following, that touches the parabola y^(2) = 4ax is-

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

Eliminate theta : x=2 sin theta, y=3 cos theta.

Whatever be the values of theta , prove that the locus of the point of intersection of the straight lines y = x tan theta and x sin^(3) theta + y cos theta = a sin^(3) theta cos theta is a circle. Find the equation of the circle.

The straight line x+ y= sqrt(2) p will touch the hyperbola 4x^(2) - 9y^(2) = 36 if-

The condition that the line ax + by + c =0 is a tangent to the parabola y^(2)= 4ax is-

Find the derivatives w.r.t. x : x = a cos theta, y = b sin theta

If x=a cos theta, y=a sin theta , then the value of (dy)/(dx) is -

The equation of the locus of the point of intersection of the straight lines x sin theta + (1- cos theta) y = a sin theta and x sin theta -(1+ cos theta) y + a sin theta =0 is:

CHHAYA PUBLICATION-TANGENT AND NORMAL -LONG ANSWER TYPE QUESTIONS
  1. If the straight line lx+my+n=0 touches the : hyperbola (x^(2))/(a^(2...

    Text Solution

    |

  2. If the straight line y= x sin alpha+ a sec alpha be a tangent ot the c...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |