Home
Class 12
MATHS
Show that xcosalpha+asin^2alpha=p touche...

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`

Text Solution

Verified by Experts

The correct Answer is:
`(a tan ^2theta-2atanalpha)`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise JEE type solved examples|1 Videos

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|20 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

Similar Questions

Explore conceptually related problems

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

Show that the line x + ny + an ^(2) =0 touches the parabola y ^(2) = 4 ax and find the point of contact.

If the straight line xcosalpha+ysinalpha=p touches the curve x y=a^2, then prove that p^2=4a^2cosalphasinalphadot

If the line x cosalpha + y sin alpha = P touches the curve 4x^3=27ay^2 , then P/a=

Show that the line x-2y + 4a = 0 touches y^(2) = 4ax.Also find the point of contact

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

Show that the focal chord, of parabola y^2 = 4ax , that makes an angle alpha with the x-axis is of length 4a cosec^2 alpha .

(i) Tangents are drawn from the point (alpha, beta) to the parabola y^2 = 4ax . Show that the length of their chord of contact is : 1/|a| sqrt((beta^2 - 4aalpha) (beta^2 + 4a^2)) . Also show that the area of the triangle formed by the tangents from (alpha, beta) to parabola y^2 = 4ax and the chord of contact is (beta^2 - 4aalpha)^(3/2)/(2a) . (ii) Prove that the area of the triangle formed by the tangents at points t_1 and t_2 on the parabola y^2 = 4ax with the chord joining these two points is a^2/2 |t_1 - t_2|^3 .

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

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

ARIHANT MATHS ENGLISH-PARABOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Show that xcosalpha+asin^2alpha=p touches the parabola y^2=4a x if pco...

    Text Solution

    |

  2. about to only mathematics

    Text Solution

    |

  3. Let P be the point (1,0) and Q be a point on the locus y^(2)=8x. The l...

    Text Solution

    |

  4. The axis of a parabola is along the line y=x and the distance of its v...

    Text Solution

    |

  5. about to only mathematics

    Text Solution

    |

  6. The locus of the vertex of the family of parabolas y=(a^3x^2)/3+(a^(2x...

    Text Solution

    |

  7. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

    Text Solution

    |

  8. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  9. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  10. Find slope of tangent to the curve if equation is x^2 + y^2 = 9

    Text Solution

    |

  11. Statement 1 : The curve y=-(x^2)/2+x+1 is symmetric with respect to th...

    Text Solution

    |

  12. The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+...

    Text Solution

    |

  13. Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0. Then, a. C1 and C2 ...

    Text Solution

    |

  14. If a parabola has the origin as its focus and the line x = 2 as the ...

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

  16. Let A and B be two distinct points on the parabola y^2=4x. If the ax...

    Text Solution

    |

  17. If two tangents drawn from a point P to the parabola y2 = 4x are at ri...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. about to only mathematics

    Text Solution

    |

  20. about to only mathematics

    Text Solution

    |

  21. about to only mathematics

    Text Solution

    |