Home
Class 12
MATHS
Find the points on the unit circle x^(2)...

Find the points on the unit circle `x^(2)+y^(2)=1` nearest and farthest from (1,1)

Text Solution

Verified by Experts

The correct Answer is:
`x=y`
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DIFFERENTIAL CALCULUS

    FULL MARKS|Exercise EXERCISE - 7.1|10 Videos

  • APPLICATIONS OF DIFFERENTIAL CALCULUS

    FULL MARKS|Exercise EXERCISE - 7.2|10 Videos

  • APPLICATIONS OF INTEGRATION

    FULL MARKS|Exercise ADDITIONAL PROBLEMS|35 Videos

Similar Questions

Explore conceptually related problems

Find the points on the circle x^2+y^2-2x+4y-20=0 which are the farthest and nearest to the point (-5,6)dot

Find the equation of the normal to the circle x^(2)+y^(2)=9 at the point (1//sqrt(2), 1// sqrt(2)) .

Find the point on the curve 3x^2-4y^2=72 which is nearest to the line 3x+2y+1=0.

The tangent and the normal lines at the point 1(sqrt3, 1) to the circle x^(2)+y^(2) = 4 and the X-axis form a triangle. The area of this triangle ( in square units ) is

Find the equation of the normal to the circle x^2+y^2=9 at the point (1/(sqrt(2)),1/(sqrt(2)))

Find the point on the hyperbola x^2/24 - y^2/18 = 1 which is nearest to the line 3x+2y+1=0 and compute the distance between the point and the line.

The point on the curve 4x^2+a^2y^2=4a^2 ; 4lta^2lt8 that is farthest from the point (0,-2) is

Find the points on the line x + y = 1 that lie at a distance 3 units from the line 5x+12y = 3.

Find the points on the ellipse (x^2)/4+(y^2)/9=1 on which the normals are parallel to the line 2x-y=1.

FULL MARKS-APPLICATIONS OF DIFFERENTIAL CALCULUS -ADDITIONAL QUESTIONS SOLVED
  1. Find the points on the unit circle x^(2)+y^(2)=1 nearest and farthest ...

    Text Solution

    |

  2. A water tank has the shape of an invertd circular cone with base radiu...

    Text Solution

    |

  3. A car A is travelling from west at 50 km/hr and car B is travelling to...

    Text Solution

    |

  4. The distance x metres travelled by a vehicle in time t seconds after t...

    Text Solution

    |

  5. At a particular instant ship A is 100 km west of ship B, ship A is sai...

    Text Solution

    |

  6. Gravel is being duped from a conveyor belt at a rate of 30 ft^(3)//min...

    Text Solution

    |

  7. Prove that the sum of the intercepts on the co-ordinate axes of any ta...

    Text Solution

    |

  8. Find the equation of normal to y = x^(3) -3x that is parallel to 2x + ...

    Text Solution

    |

  9. Prove that the curves 2x^(2)+4y^(2)=1 and 6x^(2)-12y^(2)=1 cut each ot...

    Text Solution

    |

  10. Show that the equation of the normal to the curve x=a cos ^(3) theta, ...

    Text Solution

    |

  11. If the curve y^(2) = x and xy = k are orthogonal then prove that 8k^(2...

    Text Solution

    |

  12. Verify Rolle's theorem for the following f(x) = x^(3) -3x + 3 " in "...

    Text Solution

    |

  13. Suppose that f(0) = -3, and f' (x) le 5 for all values of x how large ...

    Text Solution

    |

  14. Using Rolle's theorem find the point on the curve y=x^(2)+1,-2lexle2 w...

    Text Solution

    |

  15. Find 'C' of Lagrange's mean value theorem for the function f(x)=2x^(3)...

    Text Solution

    |

  16. Find 'C' of Lagrange's mean value theorem for the function f(x) =x^(3)...

    Text Solution

    |

  17. The Taylor's series expension of f(x)=sin x "about" x=(pi)/(2) is obta...

    Text Solution

    |

  18. Obatin the Maclaurin's series expansion for the following function . ...

    Text Solution

    |

  19. Evaluate underset(x rarr (pi)/(2))(lim) (log sin x)/((pi - 2x)^(2))

    Text Solution

    |

  20. Evaluate: underset (xrarr0) lim (cot x) ^(sin x)

    Text Solution

    |

  21. underset (x rarr infty) lim(log x^(x))/(x)

    Text Solution

    |