Home
Class 12
MATHS
A curve is represented by the equations ...

A curve is represented by the equations `x=sec^2ta n dy=cott ,` where `t` is a parameter. If the tangent at the point `P` on the curve where `t=pi/4` meets the curve again at the point `Q ,` then `|P Q|` is equal to `(5sqrt(3))/2` (b) `(5sqrt(5))/2` (c) `(2sqrt(5))/3` (d) `(3sqrt(5))/2`

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

A curve is given by the equation x=sec^(2)theta,y=cottheta. If the tangent at P where theta=pi//4 meets the curve again at Q, the [PQ] is where [.] represents the greatest integer function, "______"

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (a) (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

Show that the tangent to the curve 3x y^2-2x^2y=1a t(1,1) meets the curve again at the point (-(16)/5,-1/(20))dot

If the tangent at a point P, with parameter t, on the curve x=4t^(2)+3,y=8t^(3)-1,t in RR , meets the curve again at a point Q, then the coordinates of Q are

In a A B C , if tanA:tanB :tanC=3:4:5, then the value of sinA sinB sinC is equal to (a) 2/(sqrt(5)) (b) (2sqrt(5))/7 (2sqrt(5))/9 (d) 2/(3sqrt(5))

The points on the line x=2 from which the tangents drawn to the circle x^2+y^2=16 are at right angles is (are) (a) (2,2sqrt(7)) (b) (2,2sqrt(5)) (c) (2,-2sqrt(7)) (d) (2,-2sqrt(5))

If the line y-sqrt(3)x+3=0 cut the parabola y^2=x+2 at P and Q , then A PdotA Q is equal to [where A=(sqrt(3),0)] (a) (2(sqrt(3)+2))/3 (b) (4sqrt(3))/2 (c) (4(2-sqrt(2)))/3 (d) (4(sqrt(3)+2))/3

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

The parametric equations of a curve are given by x-sec^(2)t, y=cot t .If the tangent at P(t=(pi)/(4)) meets the curve again at Q, then show that, PQ=(3sqrt(5))/(2) .

The chord of the curve ax^(2)+bx+c=0 , joining the points x=p and x=q on the curve is parallel to the tangent to the curve at x=c where -

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. At any point on the curve 2x^2y^2-x^4=c , the mean proportional betwee...

    Text Solution

    |

  2. The x-intercept of the tangent at any arbitrary point of the curve a/(...

    Text Solution

    |

  3. A curve is represented by the equations x=sec^2ta n dy=cott , where t ...

    Text Solution

    |

  4. The two curves x=y^2,x y=a^3 cut orthogonally at a point. Then a^2 is ...

    Text Solution

    |

  5. The line tangent to the curves y^3-x^2y+5y-2x=0 and x^2-x^3y^2+5x+2y=0...

    Text Solution

    |

  6. Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) ...

    Text Solution

    |

  7. The number of point in the rectangle {(x , y)}-12lt=xlt=12a n d-3lt=yl...

    Text Solution

    |

  8. Consider a curve C : y=cos^(-1)(2x-1) and a straight line L :2p x-4y+2...

    Text Solution

    |

  9. Statement 1: The tangent at x=1 to the curve y=x^3-x^2-x+2 again meets...

    Text Solution

    |

  10. An aeroplane is flying horizontally at a height of 2/3k m with a veloc...

    Text Solution

    |

  11. Use the mean value theorem to prove e^(x)ge1+xAA x(inR)

    Text Solution

    |

  12. Find the condition for the line y= mx to cut at right angles the conic...

    Text Solution

    |

  13. Show that for the curve b y^2=(x+a)^3, the square of the sub-tangent v...

    Text Solution

    |

  14. Let a , b , c be three real numbers such that a < b < c f(x) is conti...

    Text Solution

    |

  15. Prove that the portion of the tangent to the curve (x+sqrt(a^2-y^2))...

    Text Solution

    |

  16. Let a , b , c be nonzero real numbers such that int0^1(1+cos^8x)(a x^2...

    Text Solution

    |

  17. If f is continuous and differentiable function and f(0)=1,f(1)=2, then...

    Text Solution

    |

  18. Sand is pouring from a pipe at the rate of 12c m^3//sdot The falling s...

    Text Solution

    |

  19. Let (a0)/(n+1)+(a1)/n+(a2)/(n-1)++(a(n-1))/2+an=0. Show that there e...

    Text Solution

    |

  20. If the line a x+b y+c=0 is a normal to the curve x y=1, then (a)a >0,...

    Text Solution

    |