Home
Class 12
MATHS
The curves y=a e^x and y=b e^(-x) cut or...

The curves `y=a e^x` and `y=b e^(-x)` cut orthogonally, if
(a)`a=b` (b) `a=-b` (c) `a b=1` (d) `a b=2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE IN SPACE

    RD SHARMA ENGLISH|Exercise All Questions|159 Videos

  • THE PLANE

    RD SHARMA ENGLISH|Exercise All Questions|305 Videos

Similar Questions

Explore conceptually related problems

If the curves y=2\ e^x and y=a e^(-x) intersect orthogonally, then a= (a)1//2 (b) -1//2 (c) 2 (d) 2e^2

If the curve a y+x^2=7 and x^3=y cut orthogonally at (1,\ 1) , then a is equal to (a) 1 (b) -6 (c) 6 (d) 0

If the curves ay+x^2=7 and x^3=y cut orthogonally at (1, 1) then a= (A) 1 (B) -6 (C) 6 (D) 1/6

The two curves x=y^2,x y=a^3 cut orthogonally at a point. Then a^2 is equal to 1/3 (b) 3 (c) 2 (d) 1/2

The equation of the tangent to the curve y=b e^(-x//a) at the point where it crosses the y-axis is (a)x/a-y/b=1 (b) a x+b y=1 (c)a x-b y=1 (d) x/a+y/b=1

Ifintxe^xcosx dx=a e^x(b(1-x)sinx+c xcosx)+d ,t h e n (a) a=1,b=1,c=-1 (b) a=1/2,b=-,c=1 (c) a=1,b=-1,c=1 (d) a=1/2, b=1,c=-1

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

If the family of curves y=ax^2+b cuts the family of curves x^2+2y^2-y=a orthogonally, then the value of b = (A) 1 (B) 2/3 (C) 1/8 (D) 1/4

The parabolas y^2=4ax and x^2=4by intersect orthogonally at point P(x_1,y_1) where x_1,y_1 != 0 provided (A) b=a^2 (B) b=a^3 (C) b^3=a^2 (D) none of these

Find the condition for the following set of curves to intersect orthogonally: (x^2)/(a^2)-(y^2)/(b^2)=1 and x y=c^2 (x^2)/(a^2)+(y^2)/(b^2)=1 and (x^2)/(A^2)-(y^2)/(B^2)=1.

RD SHARMA ENGLISH-TANGENTS AND NORMALS-All Questions
  1. The equaiton of the normal to the curve 3x^(2) - y^(2) = 8 which is ...

    Text Solution

    |

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

    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)a=b (b) a=...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    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 ...

    Text Solution

    |

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

    Text Solution

    |