Home
Class 12
MATHS
If the straight line xcosalpha+ysinalpha...

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`

A

`a^2 cos^2 alpha+b^2 sin^2 alpha = p^2`

B

`a^2 cos^2 alpha-b^2 sin^2 alpha = p^2`

C

`a^2 cos^2 alpha+b^2 cos^2 alpha = p^2`

D

`a^2 sin^2 alpha-b^2 sin^2 alpha = p^2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise LEVEL - 2|111 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|15 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 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^2\ cos^2alpha+b^2\ sin^2alpha=p^2 .

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

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=

If the line x Cos alpha+y Sin alpha=p touches x^(2)/a^(2)-y^(2)/b^(2)=1 then a^(2) Cos^(2)alpha-b^(2) Sin^(2)alpha=

Find the value of p so that the straight line x cos alpha + y sin alpha - p may touch the circle x^(2) + y^(2)-2ax cos alpha - 2ay sin alpha = 0 .

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

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

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

If a variable straight line x cos alpha+y sin alpha=p which is a chord of hyperbola (x^(2))/(a^(2))=(y^(2))/(b^(2))=1 (b gt a) subtends a right angle at the centre of the hyperbola, then it always touches a fixed circle whose radius, is (a) (sqrt(a^2+b^2))/(ab) (b) (2ab)/(sqrt(a^2+b^2)) (c) (ab)/(sqrt(b^2-a^2)) (d) (sqrt(a^2+b^2))/(2ab)

VMC MODULES ENGLISH-CONIC SECTIONS-LEVEL - 1
  1. If PQ is a double ordinate of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b...

    Text Solution

    |

  2. The line y=x+2 touches the hyperbola 5x^2-9y^2=45 at the point

    Text Solution

    |

  3. If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^...

    Text Solution

    |

  4. If the curves (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 (agtb) and x^(2)-y(2)=...

    Text Solution

    |

  5. about to only mathematics

    Text Solution

    |

  6. The point of intersection of two tangents to the hyperbola (x^2)/(a^2)...

    Text Solution

    |

  7. about to only mathematics

    Text Solution

    |

  8. The absolute value of slope of common tangents to parabola y^(2) = 8x ...

    Text Solution

    |

  9. Find the equations to the common tangents to the two hyperbolas (x^2)/...

    Text Solution

    |

  10. If P(a sec alpha,b tan alpha) and Q(a secbeta, b tan beta) are two poi...

    Text Solution

    |

  11. Radii of director circles of curves (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 ...

    Text Solution

    |

  12. The equation of chord of the hyperbola 25x^2- 16y^2 =400 which is bise...

    Text Solution

    |

  13. Find the locus of the midpoints of chords of hyperbola 3x^(2)-2y^(2)+4...

    Text Solution

    |

  14. about to only mathematics

    Text Solution

    |

  15. Find the locus of the midpoints of the chords of the circles x^(2)+y^(...

    Text Solution

    |

  16. If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^...

    Text Solution

    |

  17. If the straight line lx+my+n=0 be a normal to the hyperbola (x^2)/(a^2...

    Text Solution

    |

  18. The pole of the line lx+my+n=0 with respect to the hyperbola (x^(2))/(...

    Text Solution

    |

  19. If the polars of (x1,y1)" and "(x2,y2) with respect to the hyperbola (...

    Text Solution

    |

  20. The distance between the directrices of the hyperabola x=8 sec theta, ...

    Text Solution

    |