Advertisements
Advertisements
प्रश्न
Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A (4 , 1), B (6, 6) and C (8, 4).
Advertisements
उत्तर
Equation of AB
`y - y_1 = (y_2 -y_1)/(x_2-x_1) (x - x_1)`
`y - 1 = (6-1)/(6-4) (x - 4)`
`y - 1 = 5/2 (x - 4)`
2y - 2 = 5x - 20
`y = (5x)/2 - 9`
Equation of BC
`y - 6 = (4 - 6)/(8 - 6) (x - 6)`
`y - 6 = (-2)/(+2) (x - 6)`
y - 6 = -x + 6
y = -x + 12
Equation of AC
`y - 1 = (4 -1)/(8 - 4) (x - 4)`
`y -1 = 3/4 (x - 4)`
`4y - 4 = 3x - 12`
`y = (3x)/4 - 2`
संबंधित प्रश्न
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 parabola y = x2 and y = |x| .
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.
Find the area under the given curve and given line:
y = x4, x = 1, x = 5 and x-axis
Find the area between the curves y = x and y = x2
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
Using integration, find the area of the region {(x, y) : x2 + y2 ≤ 1 ≤ x + y}.
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)`.
Using definite integration, area of the circle x2 + y2 = 49 is _______.
Fill in the blank :
The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 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`
Choose the correct alternative:
Area of the region bounded by y2 = 16x, x = 1 and x = 4 and the X axis, lying in the first quadrant is ______
The area of the region bounded by the curve y2 = 4x, the X axis and the lines x = 1 and x = 4 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 circle x2 + y2 = 62
The area of the region bounded by the curve y = x IxI, X-axis and the ordinates x = 2, x = –2 is ______.
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
The area of the region bounded by the curve y = sin x and the x-axis in [–π, π] is ______.
The figure shows as triangle AOB and the parabola y = x2. The ratio of the area of the triangle AOB to the area of the region AOB of the parabola y = x2 is equal to ______.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
The area bounded by the curve `y = 3/2sqrtx`, the line x = 1 and x-axis is ______ sq. units.
What is the area of an elementary horizontal strip of length \[x\] and infinitesimally small width \[dy\]?
What is the area enclosed by the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?
