Home
Class 12
MATHS
Prove that the curve y^2=4x and x^2 +y^2...

Prove that the curve `y^2=4x and x^2 +y^2 - 6x +1=0` touches each other at thepoint `(1, 2),` find the equation of the common tangents.

Text Solution

Verified by Experts

The correct Answer is:
`x - y + 1=0`
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Exercise 6e|16 Videos

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Exercise 6f|19 Videos

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Exercise 6c|19 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

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

Show that the curvesy ^(2)=4x and x^(2)+y^(2)-6x+1=0 touch each other at (1,2). Also find the equation of the common tangent and normal.

Prove that the curve x^(2)+y^(2)=1 and y^(2)=4(x-1) touches each other.

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

The curves y=x^(2)+x+1 and 2y=x^(3)+5x touch each other at the point

The curves y=x^(3)+x+1 and 2y=x^(3)+5x touch each other at the point

find the coordinates of the points at which the circle x^(2)+y^(2)-4x-2y=4 and x^(2)+y^(2)-12x-8y=12 touch each other.Find the equation of the common tangent at the point of contact.

Show that the circles x^(2)+y^(2)-10x+4y-20=0 and x^(2)+y^(2)+14x-6y+22=0 touch each other.Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

Find the coordinates of the point at which the circles x^(2)-y^(2)-4x-2y+4=0 and x^(2)+y^(2)-12x-8y+36=0 touch each other.Also,find equations of common tangents touching the circles the distinct points.

NAGEEN PRAKASHAN-APPLICATIONS OF DERIVATIVES-Exercise 6d
  1. Find the equation of tangent of the curve y^(2) = 4x+5 which is paral...

    Text Solution

    |

  2. Find the equation of tangent of the curve 9x^(2)+16y^(2) = 144 at thos...

    Text Solution

    |

  3. Find the co-ordinates of that point on the curve x^(3)+y^(3)= a^(3) a...

    Text Solution

    |

  4. Find the co-ordinates of that point on the curvey^(2)=x^(2)(1-x) at wh...

    Text Solution

    |

  5. Find the co-ordinates of that point on the curve x^(2)/a^(2)+y^(2)/b^(...

    Text Solution

    |

  6. Prove that the equation of tangent of the ellipse x^(2)/a^(2)+y^(2)/b^...

    Text Solution

    |

  7. Find the value of n in N such that the curve (x/a)^n+(y/b)^n=2 touche...

    Text Solution

    |

  8. Show that the line d/a+y/b=1 touches the curve y=b e^(-x/a) at the poi...

    Text Solution

    |

  9. Find the point on the curve y^(2) = x at which the tangent drawn makes...

    Text Solution

    |

  10. Find the coordinates of the points on the curve y=x^2+3x+4, the tangen...

    Text Solution

    |

  11. The tangent drawn at any point of the curve sqrtx+sqrty = sqrta meets...

    Text Solution

    |

  12. If p and q are the intercept on the axis cut by the tangent of sqrt((x...

    Text Solution

    |

  13. Find the angle of intersection of the curves x y=a^2a n dx^2+y^2=2a^2

    Text Solution

    |

  14. Prove that the curvesx^(2)-y^(2)=16 and xy = 15 intersect each other a...

    Text Solution

    |

  15. If two curves ax^2 +by^2=1 and a'x^2+b'y^2=1 intersect orthogonally,th...

    Text Solution

    |

  16. Prove that the curves "x"="y"^2 and "x y"="k" intersect at right an...

    Text Solution

    |

  17. Find the equation of the tangent and the normal at the point 't, on th...

    Text Solution

    |

  18. Prove that points of the curve y^2=4a{x+asin(x/a)} at which tangents a...

    Text Solution

    |

  19. Prove that the tangents drawn on the parabola y^(2)=4axat points x = a...

    Text Solution

    |

  20. Prove that the curve y^2=4x and x^2 +y^2 - 6x +1=0 touches each other ...

    Text Solution

    |