Home
Class 12
MATHS
If the tangent at (x1,y1) to the curve x...

If the tangent at `(x_1,y_1)` to the curve `x^3+y^3=a^3` meets the curve again in `(x_2,y_2),` then prove that `(x_2)/(x_1)+(y_2)/(y_1)=-1`

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

If the tangent at (x_0,y_0) to the curve x^3+y^3=a^3 meets the curve again at (x_1,y_1) then x_1/x_0+y_1/y_0 is equal to :

If the tangent to the curve x^(3)+y^(3)=a^(3) at the point (x_(1),y_(1)) intersects the curve again at the point (x_(2),y_(2)) , then show that, (x_(2))/(x_(1))+(y_(2))/(y_(1))+1=0 .

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 (1,1) on y^2=x(2-x)^2 meets the curve again at P , then find coordinates of P .

If the join of (x_1,y_1) and (x_2,y_2) makes on obtuse angle at (x_3,y_3), then prove that (x_3-x_1)(x_3-x_2)+(y_3-y_1)(y_3-y_2)<0

If x_(1) and y_(1) be the intercepts on the x and y-axis respectively of tangent to the curve x= a cos^(3) theta, y = b sin ^(3) theta at any point theta , on the then priove that, (x_(1)^(2))/(a^(2))+(y_(1)^(2))/(b^(1))=1

Find the length of tangent to the curve y=4x^3-2x^5 at (-1,1)

If the chord of contact of tangents from a point (x_1,y_1) to the circle x^2+y^2=a^2 touches the circle (x-a)^2+y^2=a^2 , then the locus of (x_1,y_1) is :

The tangent drawn at the point (0, 1) on the curve y=e^(2x) meets the x-axis at the point -

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. If the area of the triangle included between the axes and any tangent ...

    Text Solution

    |

  2. Separate the intervals of monotonocity for the function f(x)=3cos^4x+1...

    Text Solution

    |

  3. If the tangent at (x1,y1) to the curve x^3+y^3=a^3 meets the curve aga...

    Text Solution

    |

  4. Separate the intervals of monotonocity for the function f(x)=3cos^4x+1...

    Text Solution

    |

  5. Show that the segment of the tangent to the curve y=a/2I n((a+sqrt(a^2...

    Text Solution

    |

  6. Separate the intervals of monotonocity for the function f(x)=((log)e x...

    Text Solution

    |

  7. Prove that the equation of the normal to x^(2/3)+y^(2/3)=a^(2/3) is yc...

    Text Solution

    |

  8. Discuss monotonocity of f(x)=x/(sinx)a n d g(x)=x/(tanx),where (xlt=1...

    Text Solution

    |

  9. Prove that the curves y=f(x),[f(x)>0],a n dy=f(x)sinx ,w h e r ef(x) i...

    Text Solution

    |

  10. Discuss the extremum of f(x)={x^2+x^-2}

    Text Solution

    |

  11. Tangents are drawn from the origin to curve y=sinxdot Prove that point...

    Text Solution

    |

  12. Write the maximum value of f(x)=x^(1//x) .

    Text Solution

    |

  13. Given f(x)=4-(1/2-x)^(2/3),g(x)={("tan"[x])/x ,x!=0 1,x=0 , h...

    Text Solution

    |

  14. Determine the local maxima and local minima of f(x)=x^3-6x^2+12x-8 is

    Text Solution

    |

  15. Show that the angle between the tangent at any point P and the line jo...

    Text Solution

    |

  16. Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...

    Text Solution

    |

  17. The angle between the tangents to the curves y=x^2a n dx=y^2a t(1,1) ...

    Text Solution

    |

  18. Prove that f(x)=(sinx)/x is monotonically decreasing in [0,pi/2]dot

    Text Solution

    |

  19. If the tangent at any point (4m^2,8m^2) of x^3-y^2=0 is a normal to th...

    Text Solution

    |

  20. Show that the function f(x)=4x^3-18x^2+27x-7 has neither local maxima ...

    Text Solution

    |