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)

Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    PRADEEP PUBLICATION|Exercise EXERCISE|502 Videos

  • APPLICATIONS OF INTEGRALS

    PRADEEP PUBLICATION|Exercise EXERCISE|162 Videos

Similar Questions

Explore conceptually related problems

Fill in the blanks: The curves y = 4x^2 + 2x - 8 and y = x^3 - x + 10 touch each other at the point..........

Prove that the curves xy = 4 and x^2+y^2 =8 touch each other.

Prove that the circles x^(2) +y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch at the point (3,-1)

If the circles x^2+y^2=9 and x^2+y^2+8y+c=0 touch each other, then c is equal to:

Two circles x^2 + y^2 + 2x-4y=0 and x^2 + y^2 - 8y - 4 = 0 (A) touch each other externally (B) intersect each other (C) touch each other internally (D) none of these

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

Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0 . Then,

Prove that the circle x^(2) + y^(2) + 2ax + c^(2) = 0 and x^(2) + y^(2) + 2by + c^(2) = 0 touch each other if (1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2)) .

The tangent of the curve y = 2x^2 - x + 1 is parallel to the line y = 3x + 9 at the point

PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. Show that the curve xy=a^(2)andx^(2)+y^(2)=2a^(2) touch each other.

    Text Solution

    |

  2. Prove that the curves xy = 4 and x^2+y^2 =8 touch each other.

    Text Solution

    |

  3. Prove that the curves y^2 = 4x and x^2 + y^2 - 6x + 1 = 0 touch each o...

    Text Solution

    |

  4. Find the equations of normal(s) to the curve x^2 + 2y^2 - 4x - 6y + 8 ...

    Text Solution

    |

  5. Find the coordinates of the point on the curve sqrtx + sqrty = 4 at wh...

    Text Solution

    |

  6. Show that the equations of the normal at any point theta on the curve ...

    Text Solution

    |

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

    Text Solution

    |

  8. Show that the line x/a + y/b = 1 touches the curve y = be^(x//a) at th...

    Text Solution

    |

  9. Find the equation of the tangent to the curve y=sqrt(3x-2) which is pa...

    Text Solution

    |

  10. Prove that the curves x = y^2 and xy = k cut at right angles if 8k^2 =...

    Text Solution

    |

  11. Find the condition that the curves 2x = y^2 and 2 xy = k may intersect...

    Text Solution

    |

  12. For the curve y = 5x - 2x^3, if x increases at te rate of 2units/s, th...

    Text Solution

    |

  13. In the following problems, use differentials to find the approximate v...

    Text Solution

    |

  14. In the following problems, use differentials to find the approximate v...

    Text Solution

    |

  15. In the following problems, use differentials to find the approximate v...

    Text Solution

    |

  16. In the following problems, use differentials to find the approximate v...

    Text Solution

    |

  17. In the following problems, use differentials to find the approximate v...

    Text Solution

    |

  18. In the following problems, use differentials to find the approximate v...

    Text Solution

    |

  19. In the following problems, use differentials to find the approximate v...

    Text Solution

    |

  20. If y = sin x and x change form pi/2 to 22/14, what is the approximate ...

    Text Solution

    |