English

Find the Area Enclosed Between the Parabola Y2 = 4ax and the Line Y = Mx

Advertisements
Advertisements

Question

Find the area enclosed between the parabola y2 = 4ax and the line y mx

Advertisements

Solution

The area enclosed between the parabola, y2 = 4ax, and the line, y mx, is represented by the shaded area OABO as

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Application of Integrals - Exercise 8.3 [Page 375]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 8 Application of Integrals
Exercise 8.3 | Q 6 | Page 375

RELATED QUESTIONS

Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle

`x^2+y^2=4 at (1, sqrt3)`


Find the area of the region bounded by x2 = 4yy = 2, y = 4 and the y-axis in the first quadrant.


Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.


Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line  `x = a/sqrt2`


Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.


Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`


Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12


Find the area of the smaller region bounded by the ellipse `x^2/a^2 + y^2/b^2 = 1` and the line `x/a + y/b =   1`


Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).


Find the area of the region bounded by the parabola y2 = 16x and the line x = 4. 


Find the area of the region. 

{(x,y) : 0 ≤ y ≤ x, 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .


Find the area of the region bounded by the following curves, the X-axis and the given lines:  y = x4, x = 1, x = 5


The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.


Solve the following :

Find the area of the region bounded by the curve xy = c2, the X-axis, and the lines x = c, x = 2c.


Area of the region bounded by the curve x = y2, the positive Y axis and the lines y = 1 and y = 3 is ______


Choose the correct alternative:

Area of the region bounded by the curve x2 = 8y, the positive Y-axis lying in the first quadrant and the lines y = 4 and y = 9 is ______


Choose the correct alternative:

Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______


State whether the following statement is True or False:

The area of portion lying below the X axis is negative


State whether the following statement is True or False:

The equation of the area of the circle is `x^2/"a"^2 + y^2/"b"^2` = 1


The area bounded by the parabola x2 = 9y and the lines y = 4 and y = 9 in the first quadrant is ______


The area of the region lying in the first quadrant and bounded by the curve y = 4x2, and the lines y = 2 and y = 4 is ______


Find the area of the region bounded by the curve y = (x2 + 2)2, the X-axis and the lines x = 1 and x = 3


Find the area of the region bounded by the curve y = `sqrt(36 - x^2)`, the X-axis lying in the first quadrant and the lines x = 0 and x = 6


The area bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 is ______


Area enclosed between the curve y2(4 - x) = x3 and line x = 4 above X-axis is ______.


The area of the region bounded by the curve y = x IxI, X-axis and the ordinates x = 2, x = –2 is ______.


The area of the circle `x^2 + y^2 = 16`, exterior to the parabola `y = 6x`


Area of the region bounded by y= x4, x = 1, x = 5 and the X-axis is ______.


The area (in sq.units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is ______.


The area of the region bounded by the curve y = sin x and the x-axis in [–π, π] is ______.


Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 is ______.


Area bounded by the curves y = `"e"^(x^2)`, the x-axis and the lines x = 1, x = 2 is given to be α square units. If the area bounded by the curve y = `sqrt(ℓ "n"x)`, the x-axis and the lines x = e and x = e4 is expressed as (pe4 – qe – α), (where p and q are positive integers), then (p + q) is ______.


The area bounded by the curve | x | + y = 1 and X-axis is ______.


The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×