Home
Class 12
MATHS
If x=t^(2) and y=2t then equation of the...

If `x=t^(2)` and `y=2t` then equation of the normal at `t=1` is

A

`x+y-3=0`

B

`x+y-1=0`

C

`x+y+1=0`

D

`x+y+3=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `x=t^(2)` and `y=2t`
`:.` At `t=1, x=1` and `y=2`
Now `(dy)/(dx)=(dy//dt)/(dx//dt)=2/(2t)=1/t`
At `t=1, ((dy)/(dx))_(t=1)=1`
`:.` Equation of normal is `y-2=-1(x-1)`
`impliesx+y-3=0`
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|21 Videos

  • APPLICATIONS OF DERIVATIVES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|21 Videos

  • APPLICATIONS OF DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|6 Videos

  • BINOMIAL DISTRIBUTION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|6 Videos

Similar Questions

Explore conceptually related problems

If x=t^(2) and y=2t at t=1 is

x-2=t^(2),y=2t are the parametric equations of the parabola-

Show that the locus represented by x = 1/2 a (t + 1/t) , y = 1/2 a (t - 1/t) is a rectangular hyperbola. Show also that equation to the normal at the point 't' is x/(t^(2) + 1) + y/(t^(2) - 1) = a/t .

Find the equation of the tangent and the normal at the point 't,on the curve x=a sin^(3)t,y=b cos^(3)t

Find the equations of the tangent and the normal at the point ' t ' on the curve x=a\ s in^3t , y=b\ cos^3t .

Find the equation of the tangent and the normal at the point 't' on the curve x=a(t+sint), y=a(1-cost)

The parametric equation of a parabola is x=t^(2)+1,y=2t+1. Then find the equation of the directrix.

Find the equations of the tangent and the normal to the curve x=a t^2,\ \ y=2a t at t=1 .

Find the equations of the tangent and normal to the curve x=sin3t.,y=cos2t at t=(pi)/(4)

Find the equations of the tangent and the normal to the curve x y=c^2 at (c t ,\ c//t) at the indicated points.

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-APPLICATIONS OF DERIVATIVES-MISCELLANEOUS PROBLEMS
  1. The approximate surface area of a sphere of radius 4.01 cm is

    Text Solution

    |

  2. The perimeter of a sector is a constant. If its area is to be maximum,...

    Text Solution

    |

  3. If x=t^(2) and y=2t then equation of the normal at t=1 is

    Text Solution

    |

  4. The equation of the tangent to the curve y=(1+x)^(y)+sin^(-1)(sin^(2)x...

    Text Solution

    |

  5. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  6. The radius of a cylinder is increasing at the rate of 5 cm min^(-1), s...

    Text Solution

    |

  7. Values of c of Rolle's theorem for f(x)=sin x-sin 2x on [0,pi]

    Text Solution

    |

  8. If f(x)=1/(4x^2+2x+1) , then its maximum value is 4/3 (b) 2/3 (c) 1...

    Text Solution

    |

  9. f(x)=sin+sqrt(3)cosx is maximum when x= pi/3 (b) pi/4 (c) pi/6 (d) 0

    Text Solution

    |

  10. The value of c in Lagranges theorem for the function f(x)=logsinx in t...

    Text Solution

    |

  11. For the function f(x) = x + 1/x, x in [1,3] , the value of c for me...

    Text Solution

    |

  12. The value of c in Rolle's theorem for the function f(x) = x^(3) - 3...

    Text Solution

    |

  13. If y=x^(4)-6x^(3)+13x^(2)-11x+4, then approximate valueof y when x=2.0...

    Text Solution

    |

  14. The function f(x)=2x^3-15 x^2+36 x+4 is maximum at x= (a) 3 (b) 0 (c)...

    Text Solution

    |

  15. Divide 20 into two parts such that the product of the cube of one and ...

    Text Solution

    |

  16. The function f(x)=x^(-x), ( x epsilonR) attains a maximum value at x w...

    Text Solution

    |

  17. in [0,1] , lagrange mean value theorem is NOT applicable to

    Text Solution

    |

  18. The maximum slope of the curve y=-x^3+3x^2+9x-27 is 0 (b) 12 (c) 16...

    Text Solution

    |

  19. Find local minimum value of the function f given by f(x)=3+|x|,x in R...

    Text Solution

    |

  20. The maximum value of y=a cos x+b sin x is

    Text Solution

    |