हिंदी

Find the Area of the Smaller Region Bounded by the Ellipse `X^2/9 + Y^2/4` And the Line `X/3 + Y/2 = 1`

Advertisements
Advertisements

प्रश्न

Find the area of the smaller region bounded by the ellipse `x^2/9 + y^2/4` and the line `x/3 + y/2 = 1`

Advertisements

उत्तर

The area of the smaller region bounded by the ellipse, `x^2/9 + y^2/4` , and the line, `x/3 + y/2 = 1`, is represented by the shaded region BCAB as

∴ Area BCAB = Area (OBCAO) – Area (OBAO)

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Application of Integrals - Exercise 8.3 [पृष्ठ ३७५]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 8 Application of Integrals
Exercise 8.3 | Q 8 | पृष्ठ ३७५

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

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 = 4y, y = 2, y = 4 and the y-axis in the first quadrant.


Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1.`


Find the area of the region bounded by the parabola y = x2 and y = |x| .


Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is ______.


Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0, y = 1 and y = 4


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


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


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 enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.


Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y + x = 8, x = 2, x = 4


Find the area of the region bounded by the following curve, the X-axis and the given line:

y = 2 – x2, x = –1, x = 1


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


Fill in the blank :

Area of the region bounded by x2 = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.


State whether the following is True or False :

The area bounded by the curve y = f(x), X-axis and lines x = a and x = b is `|int_"a"^"b" f(x)*dx|`.


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.


Choose the correct alternative:

Using the definite integration area of the circle x2 + y2 = 16 is ______


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 ______


Find the area of the region bounded by the curve y = `sqrt(2x + 3)`, the X axis and the lines x = 0 and x = 2


Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2


Find area of the region bounded by the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis


The ratio in which the area bounded by the curves y2 = 8x and x2 = 8y is divided by the line x = 2 is ______ 


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


The area enclosed by the parabolas x = y2 - 1 and x = 1 - y2 is ______.


Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?


The equation of curve through the point (1, 0), if the slope of the tangent to t e curve at any point (x, y) is `(y - 1)/(x^2 + x)`, is


Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:


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


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


The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m is ______.


Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0,y = 2 and y = 4.


Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.


For the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\], which expression for \[y\] is obtained before selecting the first-quadrant branch?


Why is \[y\] taken as positive for the region AOBA of the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?


What is the area enclosed by the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×