Home
Class 12
MATHS
A curve having the condition that the sl...

A curve having the condition that the slope of the tangent at some point is two times the slope of the straight line joining the same point to the origin of coordinates is a/an

A

Circle

B

Ellipse

C

Parabola

D

Hyperbola

Text Solution

Verified by Experts

The correct Answer is:
C
Let `P(x,y)` be any point on the curve
`(dy)/(dx) = 2((y-0)/(x-0))`
`int(dy)/(dx) = 2int(dx)/(x)`
`log y = 2 log x + log c`
`y = x^(2)c` parabola
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 5

    CAREER POINT|Exercise Part (C) (MATHS)|30 Videos

  • MOCK TEST 7

    CAREER POINT|Exercise PART (B) - CHEMISTRY|30 Videos

Similar Questions

Explore conceptually related problems

The curve for which the slope of the tangent at any point is equal to the ration of the abcissa to the cordinates of the point is

Find the slope of the tangent to the curve y=x^(3)-3x+2 at the point whose x-coordinate is 3 .

Find the slope of the tangent to the curve y=x^(3)-x+1 at the point whose x - coordinate is 3.

The curve in which the slope of the tangent at any point equal the ratio of the abscissa to the ordinate of the point is

The slope of the tangent at any point on a curve is lambda times the slope of the line joining the point of contact to the origin. Formulate the differential equation and hence find the equation of the curve.

Show that the slope of adiabatic curve at any point is lamda times the slope of an isothermal curve at the corresponding point.

x- If tangent drawn to the curve f(x)=x^3-9x-1 at P(x_o,f(x_o)) meets the curve again at Q.If m_A denotes the slope of tangent at A and m_op denotes the slope of the line joining O origin and a point B on the curve then: which of the following is/are correct:

Find the slope of the tangent to curve y=x^(3)-x+1 at the point whose x-coordinate is 2 .

Find the slope of the line joining the points (6, 3) and (8, 7) :

A curve passes through the point (-2, 1) and at any point (x, y) of the curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (-4, -3). Find the equation of the curve.

CAREER POINT-MOCK TEST 6-Part (C) (MATHS)
  1. The number of zeros at the end of 99^(100) - 1 is -

    Text Solution

    |

  2. If A is a square matrix of order 3 such that ||A =3, then find the val...

    Text Solution

    |

  3. Let f(x)=|{:(2cos^(2)x,,sin2x,,-sinx),(sin2x,,2sin^(2)x,,cosx),(sinx,,...

    Text Solution

    |

  4. In a three-dimensional coordinate system, P ,Q ,a n dR are images o...

    Text Solution

    |

  5. Let vec abe a unit vector and vec ba non-zero vector not parallel to v...

    Text Solution

    |

  6. The sides of a triangle have the combined equation x^2-3y^2-2x y+8y-4=...

    Text Solution

    |

  7. If (3+x^(2008)+x^(2009))^(2010)=a0+a1x+a2x^2++an x^n , then the value ...

    Text Solution

    |

  8. Given that a right angled trapezium has an inscribed circle. Prove tha...

    Text Solution

    |

  9. Find (dy)/(dx)a tx=-1,w h e n(sin"y")^(sin(pi/2x))+(sqrt(3))/2sec^(-1)...

    Text Solution

    |

  10. If e^(cos x) -e^(-cos x) = 4, then the value of cos x, is

    Text Solution

    |

  11. If -1 lt x lt 0 then sin^(-1) x equals-

    Text Solution

    |

  12. A circle of radius 2 lies in the first quadrant and touches both the a...

    Text Solution

    |

  13. Consider the set the of hyperbola xy = k, k in R. Let e(1) be the ecce...

    Text Solution

    |

  14. A man throws a fair coin number of times and gets 2 points for each he...

    Text Solution

    |

  15. Calculate mean deviation about mean from the following data: xi : ...

    Text Solution

    |

  16. The number of orded 4-tuples (x,y,z,w) where x,y,z,w in[0,10] which sa...

    Text Solution

    |

  17. Let An be the area bounded by the curve y=(tanx)^n and the lines x=0,y...

    Text Solution

    |

  18. A curve having the condition that the slope of the tangent at some poi...

    Text Solution

    |

  19. The domain of the function y=sqrt(log10(log10x)-log10(4-log10x)-log10 ...

    Text Solution

    |

  20. is continuous at x = 0, then

    Text Solution

    |