Home
Class 12
MATHS
The two curves x=y^2,x y=a^3 cut orthogo...

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`

A

`1/3`

B

3

C

2

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|16 Videos
  • APPLICATION OF DERIVATIVES

    CENGAGE ENGLISH|Exercise LINKED COMPREHENSION TYPE|8 Videos
  • APPLICATION OF DERIVATIVES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 5.8|9 Videos
  • 3D COORDINATION SYSTEM

    CENGAGE ENGLISH|Exercise DPP 3.1|11 Videos
  • APPLICATION OF INTEGRALS

    CENGAGE ENGLISH|Exercise All Questions|142 Videos

Similar Questions

Explore conceptually related problems

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 a y+x^2=7 and x^3=y cut orthogonally at (1,1) , then find the value adot

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 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

If the curves ay + x^(2) = 7 and y = x^(3) cut orthogonally at (1,1) , then the value of a is

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 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

If the circles x^2+y^2+2x+2ky+6=0 and x^2+y^2+2ky+k=0 intersect orthogonally then k equals (A) 2 or -3/2 (B) -2 or -3/2 (C) 2 or 3/2 (D) -2 or 3/2

If the circles x^2+y^2+2x+2ky+6=0 and x^2+y^2+2ky+k=0 intersect orthogonally then k equals (A) 2 or -3/2 (B) -2 or -3/2 (C) 2 or 3/2 (D) -2 or 3/2

If the lines joining the points of intersection of the curve 4x^2+9y+18 x y=1 and the line y=2x+c to the origin are equally inclined to the y-axis, the c is: -1 (b) 1/3 (c) 2/3 (d) -1/2

CENGAGE ENGLISH-APPLICATION OF DERIVATIVES-EXERCISES
  1. Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) ...

    Text Solution

    |

  2. The line tangent to the curves y^3-x^2y+5y-2x=0 and x^2-x^3y^2+5x+2y=0...

    Text Solution

    |

  3. The two curves x=y^2,x y=a^3 cut orthogonally at a point. Then a^2 is ...

    Text Solution

    |

  4. The tangent to the curve y = e ^(kx) at a point (0,1) meets the x-axis...

    Text Solution

    |

  5. The curves 4x^2+9y^2=72 and x^2-y^2=5a t(3,2) Then (a) touch each oth...

    Text Solution

    |

  6. The coordinates of a point on the parabola y^2=8x whose distance from ...

    Text Solution

    |

  7. At the point P(a,a^(n)) on the graph of y=x^(n)(n in N) in the first q...

    Text Solution

    |

  8. Let f be a continuous, differentiable, and bijective function. If the ...

    Text Solution

    |

  9. A point on the parabola y^2=18 x at which the ordinate increases at tw...

    Text Solution

    |

  10. Find the rate of change of volume of a sphere with respect to its s...

    Text Solution

    |

  11. If there is an error of k % in measuring the edge of a cube, then the ...

    Text Solution

    |

  12. A lamp of negligible height is placed on the ground l1 away from a wal...

    Text Solution

    |

  13. The function f(x)=x(x+3)e^(-(1/2)x) satisfies the conditions of Rolle'...

    Text Solution

    |

  14. The radius of a right circular cylinder increases at the rate of 0.1 ...

    Text Solution

    |

  15. A cube of ice melts without changing its shape at the uniform rate o...

    Text Solution

    |

  16. The radius of the base of a cone is increasing at the rate of 3 cm/min...

    Text Solution

    |

  17. If f(x)=x^3+7x-1, then f(x) has a zero between x=0a n dx=1 . The theor...

    Text Solution

    |

  18. Consider the function f(x)={{:(xsin(pi)/(x),"for"xgt0),(0,"for"x=0):} ...

    Text Solution

    |

  19. Let f(x)a n dg(x) be differentiable for 0lt=xlt=1, such that f(0)=0,g(...

    Text Solution

    |

  20. If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have (a...

    Text Solution

    |