Home
Class 12
MATHS
At any point of a curve sqrt(("subnorma...

At any point of a curve `sqrt(("subnormal")/("subtangent")) ` is equal to

A

the abscissa of that point

B

the ordinate of that paint

C

slope of the tangent at that point

D

slope of the normal at that point

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
Sub normal `=y (dy)/(dx), " Sub-tangent" = (y)/((dy)/(dx))`
`rArr sqrt(("sub normal")/("sub tangent"))=sqrt((y(dy)/(dx))/((y)/((dy)/(dx))))=(dy)/(dx) =` Slope of the tangent
Promotional Banner

Topper's Solved these Questions

  • TANGENTS AND NORMALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|49 Videos

  • TANGENTS AND NORMALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|42 Videos

  • SOLUTIONS OF TRIANGLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|20 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|20 Videos

Similar Questions

Explore conceptually related problems

Let a curve y=f(x),f(x)ge0, AA x in R has property that for every point P on the curve length of subnormal is equal to abscissa of p. If f(1)=3 , then f(4) is equal to

The sum of the intercepts made on the axes of coordinates by any tangent to the curve sqrt(x)+sqrt(y)=sqrt(a) is equal to

The equation of the curve whose subnormal is constant is

The abscissa of the point on the curve sqrt(x y)=a+x the tangent at which cuts off equal intercepts from the coordinate axes is -a/(sqrt(2)) (b) a//sqrt(2) (c) -asqrt(2) (d) asqrt(2)

The Curve possessing the property that the intercept made by the tangent at any point of the curve on they-axis is equal to square of the abscissa of the point of tangency, is given by

A curve y=f(x) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of the point P from the x-axis. Then the differential equation of the curve

Find the required point be P(x_1, y_1)dot The tangent to the curve sqrt(x)+sqrt(y)=4 at which tangent is equally inclined to the axes.

Find the required point be P(x_1, y_1)dot The tangent to the curve sqrt(x)+sqrt(y)=4 at which tangent is equally inclined to the axes.

If the subnormal at any point on the curve y =3 ^(1-k). x ^(k) is of constant length the k equals to :

For the equation of the curve whose subnormal is constant then,

OBJECTIVE RD SHARMA ENGLISH-TANGENTS AND NORMALS-Chapter Test
  1. At any point of a curve sqrt(("subnormal")/("subtangent")) is equal...

    Text Solution

    |

  2. The abscissa of the point on the curve ay^(2)=x^(3), the normal at whi...

    Text Solution

    |

  3. If the curves (x^2)/(a^2)+(y^2)/(b^2)=1 and (x^2)/(l^2)-(y^2)/(m^2)=1c...

    Text Solution

    |

  4. The length of normal at any point to the curve, y=c cosh(x/c) is

    Text Solution

    |

  5. If the sub-normal at any point on y=a^(1-n)x^(n) is of constant length...

    Text Solution

    |

  6. The angle of intersection of the curves y=x^(2), 6y=7-x^(3) at (1, 1),...

    Text Solution

    |

  7. The slope of the tangent to the curve x=t^2+3t-8,\ \ y=2t^2-2t-5 at ...

    Text Solution

    |

  8. What is the angle between these two curves x^3-3xy^2+2=0 and 3x^2y-y^3...

    Text Solution

    |

  9. about to only mathematics

    Text Solution

    |

  10. If y=4x-5 is a tangent to the curve y^(2)=px^(3)+q at (2, 3), then:

    Text Solution

    |

  11. The curve y-e^(xy)+x=0 has a vertical tangent at the point:

    Text Solution

    |

  12. The tangent to the curve given by x = e^(t) cos t y = e^(t) " sin t ...

    Text Solution

    |

  13. The length of the normal at t on the curve x=a(t+sint), y=a(1-cos t), ...

    Text Solution

    |

  14. For the parabola y^(2)=4ax, the ratio of the subtangent to the absciss...

    Text Solution

    |

  15. The length of the subtangent to the curve sqrt(x) +sqrt(y)=3 at the po...

    Text Solution

    |

  16. Find the euation of normal to the curve x=a( cos theta + theta sin th...

    Text Solution

    |

  17. Tangents ar drawn to y= cos x from origin then points of contact for t...

    Text Solution

    |

  18. If m denotes the slope of the normal to the curve y= -3 log(9+x^(2)) a...

    Text Solution

    |

  19. If m be the slope of the tangent to the curve e^(2y) = 1+4x^(2), then

    Text Solution

    |

  20. If the curve y=ax^(3) +bx^(2) +c x is inclined at 45^(@) to x-axis at...

    Text Solution

    |

  21. If the curve y=ax^(2)+bx+c passes through the point (1, 2) and the lin...

    Text Solution

    |