Home
Class 12
MATHS
Tangents are drawn to the ellipse x^2+2y...

Tangents are drawn to the ellipse `x^2+2y^2=2`, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

A

`1/(2x^2)+1/(4y^2)=1`

B

`1/(4x^2)+1/(2y^2)=1`

C

`x^2/2+y^2/4=1`

D

`x^2/4+y^2/2=1`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the common tangent in the first quadrant of the circle x^2+y^2=16 and the ellipse x^2/25+y^2/4=1 .Also find the length of the intercept of the tangent between the coordinates axes.

Locus of mid-point of the portionof the line x cos alpha + y sin alpha =p between the coordinate axes is-

Through a fixed point (h, k) secants are drawn to the circle x^2 +y^2 = r^2 . Then the locus of the mid-points of the secants by the circle is

A tangent is drawn at the point (3 sqrt(3) cos theta, sin theta) (0 lt theta lt (pi)/(2)) to the ellipse x^(2) + 27y^(2)=27 , then the least value of the sum of the intercepts on the coordinate axes by this tangent is attained when the value of theta is-

If from a point P , tangents PQ and PR are drawn to the ellipse (x^2)/2+y^2=1 so that the equation of Q R is x+3y=1, then find the coordinates of Pdot

Prove that the locus of the mid - point of the portion of the line segment made by the straigh line xcostheta+ysintheta=p upon the coordinate axes is p^(2)(x^(2)+y^(2))=4x^(2)y^(2) .

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at A and B . The locus of the point of intersection of tangents at A and B to the circle x^2+y^2=9 is (a) x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 (c) y^2-x^2=((27)/7)^2 (d) none of these

Find the locus of the point of intersection of the perpendicular tangents of the curve y^2+4y-6x-2=0 .

A moving straight line always passes through the point (h,k) . Prove that the locus of the middle point of the portion of the straight line intercepted between the axes of coordinates is , (h)/(x)+(k)/(y)=2 .

Find the locus of the mid-point of the portion of the line x cosalpha+ysinalpha=4 intercepted between the axes of coordinates.

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. The minimum value of logax+logxa,0ltxlta, is

    Text Solution

    |

  2. The sides of the rectangle of the greatest area, that can be inscribed...

    Text Solution

    |

  3. Tangents are drawn to the ellipse x^2+2y^2=2, then the locus of the mi...

    Text Solution

    |

  4. The tangent to the curve y=e^x drawn at the point (c,e^c) intersects t...

    Text Solution

    |

  5. The curves x^2/a+y^2/b=1and x^2/a1+y^2/b1=1 will cut orthogonally if ...

    Text Solution

    |

  6. If the tangent to the curve 2y^3=ax^2+x^3 at the point (a,a) cuts off ...

    Text Solution

    |

  7. The normal to the curve x=a(costheta+thetasintheta),y=a(sintheta-theta...

    Text Solution

    |

  8. The distance between the origin and the normal to the curve y=e^(2x)+x...

    Text Solution

    |

  9. Let g(x)={(2e,if,xle1),(log(x-1),if,xgt1):} The equation of the normal...

    Text Solution

    |

  10. The intercepts on x-axis made by tangents to the curve, oversetxunders...

    Text Solution

    |

  11. The Rolle's thorem is applicable in the interval -1lexle1 for the func...

    Text Solution

    |

  12. A value of 'c' for which the conclusion of mean value theorem holds fo...

    Text Solution

    |

  13. A value of ‘c’ for which conclusion of Mean Value Theorem holds for th...

    Text Solution

    |

  14. If f(x)=x^3+bx^2+cx+d and 0ltb^2ltc then in (-oo,oo)

    Text Solution

    |

  15. If f is a twice differentiable function such that f''(x)=-f(x),f'(x)=g...

    Text Solution

    |

  16. Consider a function y = f(x) defined parametrically asy=2t+t, x=t^2 fo...

    Text Solution

    |

  17. The range of value of x for which the function f(x)=x/logx,xgt0 and "x...

    Text Solution

    |

  18. If F(x)=|[x,x^2,x^3],[1,2x,3x^2],[0,2,6x]| , then F'(x) is

    Text Solution

    |

  19. The least value of the function f(x)= cos^(-1)x^2 in the interval [-1/...

    Text Solution

    |

  20. If a function is everywhere continuous and differentiable such that f'...

    Text Solution

    |