Home
Class 12
MATHS
The line y=m x+1 is a tangent to the ...

The line `y=m x+1` is a tangent to the curve `y^2=4x` , if the value of `m` is (a) 1 (b) 2 (c) 3 (d) 1/2

Text Solution

Verified by Experts

Lets put y=mx+1 in `y^2=4x` we get
`(mx+1)^2=4x`
⇒`m^2x^2+1+2mx−4x=0`
Tangent touches a curve at one point so descriminant of the equation should be zero.
⇒`(2m−4)^2−4×1×m^2=0`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE IN SPACE

    RD SHARMA|Exercise Solved Examples And Exercises|134 Videos

  • THE PLANE

    RD SHARMA|Exercise Solved Examples And Exercises|301 Videos

Similar Questions

Explore conceptually related problems

The line y=mx+1 is a tangent to the curve y^2=4x if the value of m is (A) 1 (B) 2 (C) 3 (D) 1/2 .

The line y=mx+1 is a tangent to the curve y^(2)=4x if the value of m is (A) 1(B)2(C)3(D)(1)/(2)

The line y=x+1 is a tangent to the curve y^(2)=4x at the point :

The line y=x+1 is a tangent to the curve y^(2)=4x at the point:

The line y=x+1 is tangent to the curve y^(2)=4x at the point :

If the line y=mx+1 is tangent to the parabola y^(2)=4x, then find the value of m .

The line y" "=" "x" "+" "1 is a tangent to the curve y^2=4x at the point (A) (1," "2) (B)(2," "1) (C) (1," "" "2) (D) (" "1," "2)

If the line joining the points (0,3) and (5,-2) is a tangent to the curve y=(C)/(x+1), then the value of c is 1(b)-2(c)4(d) none of these

The line y=mx+1 is a tangent to the parabola y^2 = 4x if (A) m=1 (B) m=2 (C) m=4 (D) m=3

If m is the slope of the tangent to the curve e^(y)=1+x^(2) , then

RD SHARMA-TANGENTS AND NORMALS-Solved Examples And Exercises
  1. The equation of the normal to the curve 3x^2-y^2=8 which is paralle...

    Text Solution

    |

  2. The equation of tangent at those points where the curve y=x^2-3x+2 ...

    Text Solution

    |

  3. The slope of the tangent to the curve x=t^2+3t-8,\ \ y=2t^2-2t-5 at...

    Text Solution

    |

  4. At what points the slope of the tangent to the curve x^2+y^2-2x-3=0...

    Text Solution

    |

  5. The angle of intersection of the curves x y=a^2 and x^2-y^2=2a^2 is...

    Text Solution

    |

  6. If the curve a y+x^2=7 and x^3=y cut orthogonally at (1,\ 1) , then a ...

    Text Solution

    |

  7. If the line y=x touches the curve y=x^2+b x+c at a point (1,\ 1) then ...

    Text Solution

    |

  8. The slope of the tangent to the curve x=3t^2+1 , y=t^3-1 at x=1 is ...

    Text Solution

    |

  9. The curves y=a e^x and y=b e^(-x) cut orthogonally, if a=b (b) a=-b (c...

    Text Solution

    |

  10. The equation of the normal to the curve x=a\ cos^3theta,\ \ y=a\ s ...

    Text Solution

    |

  11. If the curves y=2\ e^x and y=a e^(-x) intersect orthogonally, then ...

    Text Solution

    |

  12. The point on the curve y=6x-x^2 at which the tangent to the curve i...

    Text Solution

    |

  13. The angle of intersection of the parabola y^2=4\ a x and x^2=4a y a...

    Text Solution

    |

  14. The angle of intersection of the curves y=2\ s in^2x and y=cos2\ x ...

    Text Solution

    |

  15. Any tangent to the curve y=2x^7+3x+5 (a) is parallel to x-axis ...

    Text Solution

    |

  16. The point on the curve 9y^2=x^3 , where the normal to the curve mak...

    Text Solution

    |

  17. The slope of the tangent to the curve x=t^2+3t-8,\ \ y=2t^2-2t-5 at...

    Text Solution

    |

  18. The line y=m x+1 is a tangent to the curve y^2=4x , if the value of...

    Text Solution

    |

  19. The normal at the point (1,1) on the curve 2y+x^2=3is(A) x + y = 0 (B)...

    Text Solution

    |

  20. The normal to the curve x^2=4ypassing (1,2) is(A) x + y = 3 (B) x y ...

    Text Solution

    |