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)
APPEARS IN
संबंधित प्रश्न
Using integration find the area of the region {(x, y) : x2+y2⩽ 2ax, y2⩾ ax, x, y ⩾ 0}.
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 y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.
Find the area of the region bounded by the parabola y = x2 and y = |x| .
Find the area bounded by the curve x2 = 4y and the line x = 4y – 2
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
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 \[\frac{x^2}{9} + \frac{y^2}{4} = 1\] and the line \[\frac{x}{3} + \frac{y}{2} = 1 .\]
Find the area of the region.
{(x,y) : 0 ≤ y ≤ x2 , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .
Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9 "at" (-1,2sqrt2)`.
Find the area of the region bounded by the following curves, the X-axis, and the given lines:
y = `sqrt(6x + 4), x = 0, x = 2`
Using definite integration, area of the circle x2 + y2 = 49 is _______.
State whether the following is True or False :
The area bounded by the curve x = g (y), Y-axis and bounded between the lines y = c and y = d is given by `int_"c"^"d"x*dy = int_(y = "c")^(y = "d") "g"(y)*dy`
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|`.
If the curve, under consideration, is below the X-axis, then the area bounded by curve, X-axis and lines x = a, x = b is positive.
The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x) "d"x`
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 circle x2 + y2 = 16 is ______
The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant is ______
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5
Find area of the region bounded by the parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3
Find the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5
The ratio in which the area bounded by the curves y2 = 8x and x2 = 8y is divided by the line x = 2 is ______
Area under the curve `y=sqrt(4x+1)` between x = 0 and x = 2 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 (in sq. units) of the region {(x, y) : y2 ≥ 2x and x2 + y2 ≤ 4x, x ≥ 0, y ≥ 0} 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.
For an area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\], which strips are used?
Which expression gives physical area when the curve \[y=f(x)\] lies below the \[x\]-axis from \[x=a\] to \[x=b\]?
Why cannot a curve crossing the \[x\]-axis within \[a,b\] be integrated directly from \[a\] to \[b\] to obtain total area?
A curve crosses the \[x\]-axis, forming area \[A_1\] below the axis and area \[A_2\] above the axis. What is its total area?
Why is \[y\] taken as positive for the region AOBA of the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?
Which integral represents the enclosed area of the ellipse after using the positive first-quadrant value of \[y\]?
