Home
Class 11
MATHS
If the line y=m x+1 is tangent to the pa...

If the line `y=m x+1` is tangent to the parabola `y^2=4x ,` then find the value of `mdot`

A

1

B

2

C

4

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
If y = mx + 1 touches the parabola `y^(2)=4x`, then the equation
must have equal roots.
`:." "4(m-2)^(2)=4m^(2)rArrm=1`
ALITER We know tha t = mx + c touches `y^(2)=4ax,` if c = a/m.
`:." y = mx + 1 will touch "y^(2)=4x,` if
`1=1/mrArrm=1" "["Using : c"=a/m]`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|66 Videos

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise SECTION-I (SOLVED MCQs EXAMPLE)|1 Videos

  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

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

If the line x-y+k =0 is a tangent to the parabola x^(2) = 4y then k = ?

Statement I The line y=mx+a/m is tangent to the parabola y^2=4ax for all values of m. Statement II A straight line y=mx+c intersects the parabola y^2=4ax one point is a tangent line.

Show that the line x- y +4=0 is tangent to the parabola y^(2)= 16x . Find the point of contact.

If the line x+y=a touches the parabola y=x-x^2, then find the value of adot

If the line x+y=a touches the parabola y=x-x^2, then find the value of a .

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

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

If m is the slope of common tangent lo circle x^(2)+y^(2 )= c^(2) and the parabola y^(2 )= 4ax then find the value of m^(2)

If y=mx+4 is common tangent to parabolas y^(2)=4x and x^(2)=2by . Then value of b is

OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Chapter Test
  1. If the line y=m x+1 is tangent to the parabola y^2=4x , then find the ...

    Text Solution

    |

  2. If y=2x+k is a tangent to the curve x^(2)=4y, then k is equal to

    Text Solution

    |

  3. The normal drawn at a point (a t1 2,-2a t1) of the parabola y^2=4a x m...

    Text Solution

    |

  4. The mid-point of the chord 2x+y-4=0 of the parabola y^(2)=4x is

    Text Solution

    |

  5. The two ends of latusrectum of a parabola are the points (3, 6) and (-...

    Text Solution

    |

  6. Prove that the locus of the middle points of all chords of the parabol...

    Text Solution

    |

  7. The focus of the parabola x^2-8x+2y+7=0 is

    Text Solution

    |

  8. The point of contact of the line x-2y-1=0 with the parabola y^(2)=2(x-...

    Text Solution

    |

  9. Find the number of distinct normals that can be drawn from (-2,1) to t...

    Text Solution

    |

  10. At what point on the parabola y^2=4x the normal makes equal angle with...

    Text Solution

    |

  11. Three normals to the parabola y^2= x are drawn through a point (C, O) ...

    Text Solution

    |

  12. The normal chord of a parabola y^2= 4ax at the point P(x1, x1) subten...

    Text Solution

    |

  13. AB, AC are tangents to a parabola y^2=4ax; p1, p2, p3 are the lengths...

    Text Solution

    |

  14. The circles on the focal radii of a parabola as diameter touch: A) th...

    Text Solution

    |

  15. If the normals from any point to the parabola y^2=4x cut the line x=2 ...

    Text Solution

    |

  16. about to only mathematics

    Text Solution

    |

  17. The equation of the tangent to the parabola y^(2)=8x which is perpendi...

    Text Solution

    |

  18. the tangent drawn at any point P to the parabola y^2= 4ax meets the di...

    Text Solution

    |

  19. about to only mathematics

    Text Solution

    |

  20. The parabola y^(2)=4ax passes through the point (2,-6). Find the lengt...

    Text Solution

    |

  21. A variable circle passes through the fixed point (2, 0) and touches y-...

    Text Solution

    |