Home
Class 12
MATHS
The area of the circle x^2+y^2=16 exteri...

The area of the circle `x^2+y^2=16` exterior to the parabola `y^2=6x` is (A) `4/3(4pi-sqrt(3))` (B) `4/3(4pi+sqrt(3))`(C) `4/3(8pi-sqrt(3))` (D) `4/3(8pi+sqrt(3))`

Text Solution

AI Generated Solution

To find the area of the circle \(x^2 + y^2 = 16\) that is exterior to the parabola \(y^2 = 6x\), we will follow these steps: ### Step 1: Identify the equations The equation of the circle is: \[ x^2 + y^2 = 16 \] The equation of the parabola is: ...
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT|Exercise SOLVED EXAMPLES|15 Videos

  • APPLICATION OF INTEGRALS

    NCERT|Exercise EXERCISE 8.2|7 Videos

  • APPLICATION OF INTEGRALS

    NCERT|Exercise EXERCISE 8.2|7 Videos

  • APPLICATION OF DERIVATIVES

    NCERT|Exercise EXERCISE 6.1|18 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise QUESTION|3 Videos

Similar Questions

Explore conceptually related problems

If 0lt=xlt=pi/3 then range of f(x)=sec(pi/6-x)+sec(pi/6+x) is (a)(4/(sqrt(3)),oo) (b) (4/(sqrt(3)),oo) (c)(0,4/(sqrt(3))) (d) (0,4/(sqrt(3)))

If the distance between the centers of two circles of unit radii is 1 the common area of the circles is 1) (2 pi)/(3)-sqrt(3) 2) (2 pi)/(3)+sqrt(3) 3) (2 pi)/(3)-(sqrt(3))/(2) 4) (2 pi)/(3)(sqrt(3))/(3)

the length of intercept made by the line sqrt2x-y-4sqrt2=0 on the parabola y^2=4x is equal to (a) 6sqrt3 (b) 4sqrt3 (c) 8sqrt2 (d) 6sqrt2

The area ( in sq.units) of the region {(x,y):y^(2)>=2x and x^(2)+y^(2) =0} is :(A)pi-(4)/(3)(B)pi-(8)/(3)(C)pi-(4sqrt(2))/(3) (D) pi-(2sqrt(2))/(3)

The shortest distance between line y-x=1 and curve is : (1)(sqrt(3))/(4) (2) (3sqrt(2))/(8) (3) (8)/(3sqrt(2))(4)(4)/(sqrt(3))

If the area of a square is same as the area of the circle, then the ratio of their perimeters, in terms of pi , is (a) pi\ :sqrt(3) (b) 2\ :sqrt(pi) (c) 3\ :pi (d) pi\ :sqrt(2)

The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal, is (a) pi\ :sqrt(2) (b) pi\ :sqrt(3) (c) sqrt(3)\ :pi (d) sqrt(2)\ :pi

The shortest distance between the line yx=1 and the curve x=y^(2) is (A)(3sqrt(2))/(8) (B) (2sqrt(3))/(8) (C) (3sqrt(2))/(5) (D) (sqrt(3))/(4)

The tangent to the graph of the function y=f(x) at the point with abscissae x=1, x=2, x=3 make angles pi/6,pi/3 and pi/4 respectively. The value of int_1^3f\'(x)f\'\'(x)dx+int_2^3f\'\'(x)dx is (A) (4-3sqrt(3))/3 (B) (4sqrt(3)-1)/(3sqrt(3)) (C) (4-3sqrt(3))/2 (D) (3sqrt(3)-1)/2

A triangle is inscribed in a circle.The vertices of the triangle divide the circle into three arcs of length 3,4 and 5 ,then the area of the triangle is equal to 1.(9sqrt(3)(1+sqrt(3)))/(pi^(2)) 2.(9sqrt(3)(sqrt(3)-1))/(pi^(2)) 3.(9sqrt(3)(1+sqrt(3)))/(2 pi^(2)) 4.(9sqrt(3)(sqrt(3)-1))/(2 pi^(2))

NCERT-APPLICATION OF INTEGRALS-MISCELLANEOUS EXERCISE
  1. The area of the circle x^2+y^2=16 exterior to the parabola y^2=6x is (...

    Text Solution

    |

  2. Using the method of integration find the area bounded by the curve |x...

    Text Solution

    |

  3. Find the area bounded by the curve y = sin x between x = 0 and x=2pi.

    Text Solution

    |

  4. Using the method of integration find the area of the triangle ABC, co...

    Text Solution

    |

  5. Area bounded by the curve y=x^3, the x-axis and the ordinates x = 2a...

    Text Solution

    |

  6. Find the area of the region lying in the first quadrant and bounded b...

    Text Solution

    |

  7. Find the area bounded by curves {(x ,y):ygeqx^2 and y = | x |}

    Text Solution

    |

  8. Find the area of the region {(x ,y): y^2lt=4x ,4x^2+4y^2lt=9}

    Text Solution

    |

  9. Find the area of the smaller region bounded by the ellipse (x^2)/9+(y...

    Text Solution

    |

  10. Find the area of the smaller region bounded by the ellipse (x^2)/(a^2...

    Text Solution

    |

  11. Sketch the graph of y = |x + 3|and evaluateint-6 ^0|x+3|dx.

    Text Solution

    |

  12. Find the area enclosed between the parabola y^2=4a xand the line y = ...

    Text Solution

    |

  13. Find the area enclosed by the parabola 4y=3x^2 and the line 2y=3x+12.

    Text Solution

    |

  14. Find the area under the given curves and given lines:(i) y=x^2,x = 1,...

    Text Solution

    |

  15. the area between the curves y= x^2 and y =4x is

    Text Solution

    |

  16. Using the method of integration find the area of the region bounded b...

    Text Solution

    |

  17. Find the area of the region enclosed by the parabola x^(2)=y and the l...

    Text Solution

    |

  18. The area bounded by the curve y = x | x |, x-axis and the ordinates x...

    Text Solution

    |

  19. The area bounded by the y-axis, y = cos xand y = s in xwhen 0lt=xlt=p...

    Text Solution

    |