Home
Class 12
MATHS
Prove that the curves y^(2)=4x and x^(2)...

Prove that the curves `y^(2)=4x` and `x^(2)+y^(2)-6x+1=0` touch each other at the point (1, 2).

Text Solution

Verified by Experts

The correct Answer is:
`m_(1)=m_(2)`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (LONG ANSWER TYPE QUESTIONS)|10 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (OBJECTIVE TYPE TYPE QUESTIONS)|25 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK|51 Videos

  • ANNUAL EXAMINATION :SAMPLE PAPER

    KUMAR PRAKASHAN|Exercise PART-B ( SECTION-C)|10 Videos

  • APPLICATION OF INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER ( SECTION -D)|2 Videos

Similar Questions

Explore conceptually related problems

Show that the curves xy=a^(2) and x^(2)+y^(2)=2a^(2) touch each other.

The curves y=4x^(2)+2x-5 and y=x^(3)-x+13 touch each other at the point …………..

Prove that the curves x^(2)+y^(2)=ax and x^(2)+y^(2)=by are cuts orthogonally.

Prove that the curves y^(2) =4x" and "x^(2)= 4y divide the area of the square bounded by x= 0, x= 4, y =4 and y= 0 into three equal parts.

If the circles x^(2)+y^(2)+4x+8y=0andx^(2)+y^(2)+8x+2ky=0 touch each other , then =.........

Prove that the curves y^2 = 4x and x^2 = 4y divide the area of the square bounded by x=0, x=4 y=4 and y=0 into three equal parts .

If the circles x^(2) + y^(2) = a^(2) and x^(2) + y^(2) - 6x - 8y + 9 = 0 touches each other externally, then a = …….

Consider the two curves C_1 ; y^2 = 4x , C_2 : x^2 + y^2 - 6x + 1 = 0 then :

Find the equations of the tangents drawn to the curve y^(2)-2x^(3)-4y+8=0 from the point (1, 2).

KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)
  1. Find an angle theta, where 0 lt theta lt (pi)/(2) which increases twic...

    Text Solution

    |

  2. Find the approximate value of (1.999)^(5).

    Text Solution

    |

  3. Find the approximate volume of metal in a hollow spherical shell whose...

    Text Solution

    |

  4. A man, 2m tall, walks at the rate of 1(2)/(3) m/s towards a street lig...

    Text Solution

    |

  5. A swimming pool is to be drained for cleaning. If L represents the num...

    Text Solution

    |

  6. The volume of a cube increases at a consant rate. Prove that the incre...

    Text Solution

    |

  7. x and y are the sides of two squares such that y=x-x^(2). Find the rat...

    Text Solution

    |

  8. Find the condition that the curves 2x=y^(2) and 2xy = k intersect orth...

    Text Solution

    |

  9. Show that the curves xy=a^(2) and x^(2)+y^(2)=2a^(2) touch each other.

    Text Solution

    |

  10. Find the co-ordinates of the point on the curve sqrt(x)+sqrt(y)=4 at w...

    Text Solution

    |

  11. Find the angle of intersection of the curves y = 4-x^(2) and y=x^(2).

    Text Solution

    |

  12. Prove that the curves y^(2)=4x and x^(2)+y^(2)-6x+1=0 touch each other...

    Text Solution

    |

  13. Find the equation of the normal lines to the curve 3x^(2)-y^(2)=8 whic...

    Text Solution

    |

  14. At what points on the curve x^(2)+y^(2)-2x-4y+1=0, the tangents are pa...

    Text Solution

    |

  15. Show that a point at which the line (x)/(a)+(y)/(b)=1 touches to the c...

    Text Solution

    |

  16. Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x^(2))-x) is increasing in R.

    Text Solution

    |

  17. Show that for a ge 1, f(x)=sqrt(3)sin x - cos x - 2ax + b is decreasin...

    Text Solution

    |

  18. Show that f(x)=tan^(-1)(sin x + cos x) is an increasing function in (0...

    Text Solution

    |

  19. At what point, the slope of the curve y=-x^(3)+3x^(2)+9x-27 is maximum...

    Text Solution

    |

  20. Prove that f(x)=sin x+3^(1/2) cos x has maximum value at x=(pi)/(6)

    Text Solution

    |