Home
Class 12
MATHS
Find the point on the parabola y^(2) = 2...

Find the point on the parabola `y^(2) = 2x` that is closest to the point (1, 4)

Text Solution

Verified by Experts

The correct Answer is:
2,2
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DIFFERENTIAL CALCULUS

    PREMIERS PUBLISHERS|Exercise Problems For Practice (Choose the correct answer)|40 Videos

  • APPLICATIONS OF INTEGRATION

    PREMIERS PUBLISHERS|Exercise Answer the following questions.|18 Videos

Similar Questions

Explore conceptually related problems

Find a point on the parabola y^(2) = 2 that is closest to the point (1, 32)

Find the locus of the midpoint of chords of the parabola y^2=4a x that pass through the point (3a ,a)dot

Find the points on the parabola y^2-2y-4x=0 whose focal length is 6.

Find the equation of tangents of the parabola y^2=12 x , which passes through the point (2, 5).

(i) Find the points of intersection of the parabola y ^(2) = 8x and the line y = 2x . (ii) Find, using integration, the area enclosed between the line and the parabola.

The area (in sq units) of the smaller of the two circles that touch the parabola, y^(2) = 4x at the point (1,2) and the X-axis is

Find the coordinates of a point the parabola y^(2)=8x whose distance from the focus is 10.

Find the coordinates of points on the parabola y^2=8x whose focal distance is 4.

Find the equations of the tangent and normal to the parabola y^(2) = 4ax at the point (at^(2) , 2at).

Find the equation of the tangent to the parabola y^2=8x having slope 2 and also find the point of contact.

PREMIERS PUBLISHERS-APPLICATIONS OF DIFFERENTIAL CALCULUS-Problems For Practice (Answer the following question)
  1. Verify mean value theorem for the function f(x) = x^(3) - 5x^(2) 2x i...

    Text Solution

    |

  2. Expand f(x) = e^(3x) on a maclaurin's series

    Text Solution

    |

  3. Evaluate: underset(x rarr 2)(lim) (sin pi x)/(2 -x)

    Text Solution

    |

  4. Evaluate: underset(x rarr oo)(lim) (x^((1)/(2)) -2 tan^(-1) ((1)/(x)))...

    Text Solution

    |

  5. Evaluate: underset(x rarr 0)(lim) x^(sin x)

    Text Solution

    |

  6. Prove , using mean value theorem, that |sin alpha -sin beta | le| alph...

    Text Solution

    |

  7. Expand f(x) = (1)/(x) about x =2 upto four terms

    Text Solution

    |

  8. Evaluate underset(theta rarr 0)(lim) (1- cos m theta)/(1- cos n theta)

    Text Solution

    |

  9. Evaluate: underset(xrarr0)lim xlog x

    Text Solution

    |

  10. Determine for which values of x the function y = (x-2)/(x + 1), x ne -...

    Text Solution

    |

  11. Discuss the monotonicity of f(x) = 2x^(3) - 15x^(2) + 36x + 1

    Text Solution

    |

  12. Find the critical number and stationary point f(x) = 2x - 3x^(2)

    Text Solution

    |

  13. Find the absolute extreme for f(x) = 1 - 2x - x^(2) in (-4,1)

    Text Solution

    |

  14. Find the local maximum and local minimum of f(x) = 2x^(3) + 5x^(2) - 4...

    Text Solution

    |

  15. Find the absolute extreme of the function f(x) = 2 cos x in [0, 2pi]

    Text Solution

    |

  16. Find the points of inflection of y = x^(4) - 6x^(2) + 8x -1

    Text Solution

    |

  17. Obtain Maclaurin's series for f(x) = log sec x

    Text Solution

    |

  18. Resistance to motion F of a moving vehicle is given by F = (5)/(x) + 1...

    Text Solution

    |

  19. Find the point on the parabola y^(2) = 2x that is closest to the point...

    Text Solution

    |

  20. Find the asymptotes of the function f(x) = (1)/(x + 1)

    Text Solution

    |