Home
Class 12
MATHS
The point on the curve y^(2)=x the tange...

The point on the curve `y^(2)=x` the tangent at which makes an angle `45^(@)` with X-axis is

A

`(1/4,1/2)`

B

`(1/2,1/4)`

C

`(1/2,-1/2)`

D

`(1/2,1/2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `y^(2)=x`…………i
`implies2y(dy)/(dx)=1`
`implies(dy)/(dx)=1/(2y)=` slope
Also slope `tan 45^(@)=1`
`implies1/(2y)=1impliesy=1/2`
From Eq. (i) if `y=1/2`,
then `x=1/4`
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 12

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

  • PRACTICE SET 14

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

Similar Questions

Explore conceptually related problems

The point on the curve y^(2)=8x the tangent at which makes an angle 30^(@) with X -axis

The point on the curve, y^(2)=2x ,the tangent at which makes an angle of 45^(@) with x -axis will be given by

Find the point on the curve y^(2)=ax the tangent at which makes an angle of 45^(@) with the x-axis.

Find the point on the curve y^2=4x the tangent at which makes an angle 60^@ with X-axis.

The point on the curve y^(2)=x , where the tangent makes an angle of (pi)/(4) with x-axis is :

Write the coordinates of the point on the curve y^2=x where the tangent line makes an angle pi/4 with x-axis.

Find the point on the curve y^(2) = x at which the tangent drawn makes an angle of 45^(@) from X-axis.

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 13-PAPER II OBJECTIVE TYPE
  1. If y=x-x^2, then the derivative of y^2 w.r.t x^2 is

    Text Solution

    |

  2. If f'(x)=g(x) and g'(x)=-f(x) for all x and f(2)=4=f'(2) then f^(2)(4)...

    Text Solution

    |

  3. The point on the curve y^(2)=x the tangent at which makes an angle 45^...

    Text Solution

    |

  4. The smallest circle with centre on Y-axis and passing through the poin...

    Text Solution

    |

  5. The function f(x)=x(x+3)e^(-(1/2)x) satisfies the conditions of Rolle'...

    Text Solution

    |

  6. For what values of x the function f(x)=x^(4)-4x^(3)+40 si monotonic de...

    Text Solution

    |

  7. If a is a positive number such that the arithmatic mean of a and 2 exc...

    Text Solution

    |

  8. A line passing through origin and is perpendicular to two given lines ...

    Text Solution

    |

  9. If A and B are two sets, then (AuuB)'uu(A'nnB) is equal to

    Text Solution

    |

  10. If a relation R on the set N of natural numbers is defined as (x,y)hAr...

    Text Solution

    |

  11. If 5cos2 theta+2 "cos"^(2) (theta)/2+1=0, when (0 lt thetaltpi) the th...

    Text Solution

    |

  12. If in DeltaABC,a=12cm, b=12cm and c=5cm then distance from a to side B...

    Text Solution

    |

  13. The value of cos[2 tan^(-1)(-7)] is

    Text Solution

    |

  14. Solution of the differential equation x(dy)/(dx)=y+sqrt(x^(2)+y^(2)), ...

    Text Solution

    |

  15. The differential equation satistied by the family of curves y=axcos(1/...

    Text Solution

    |

  16. The value of sqrt(2)int(sinx)/(sin(x-(pi)/(4)))dx , is

    Text Solution

    |

  17. The slope of the tangent to a curve y=f(x) at (x,f(x)) is 2x+1. If the...

    Text Solution

    |

  18. The area of the region bounded by the parabola (y-2)^(2) = x- 1, the t...

    Text Solution

    |

  19. If a line makes an angle of pi/4 with the positive directions of ea...

    Text Solution

    |

  20. Find the ratio in which the line joining (2,4,5) and (3,5,4) is divide...

    Text Solution

    |