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The area of the region bounded by the parabola (y – 2)2 = x –1, the tangent of the parabola at the point (2, 3) and the x-axis is:
- a)6
- b)9
- c)12
- d)3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The area of the region bounded by the parabola (y – 2)2 = x &nda...
The given parabola is (y – 2)2 = x – 1 Vertex (1, 2) and it meets x–axis at (5, 0) Also it gives y2 – 4y – x + 5 = 0
So, that equation of tangent to the parabola at (2, 3) is
So, that equation of tangent to the parabola at (2, 3) is
which meets x-axis at (– 4, 0).
In the figure shaded area is the required area.
Let us draw PD perpendicular to y – axis.
In the figure shaded area is the required area.
Let us draw PD perpendicular to y – axis.
Then required area = Ar ΔBOA + Ar (OCPD) – Ar (ΔAPD)
Most Upvoted Answer
The area of the region bounded by the parabola (y – 2)2 = x &nda...
The equation of the parabola is y = x^2. To find the area bounded by the parabola, we need to integrate the area under the curve between the x-values where the curve intersects the x-axis.
To find the x-values where the curve intersects the x-axis, we set y = 0:
0 = x^2
x = 0
So, the parabola intersects the x-axis at x = 0.
To find the area bounded by the parabola, we integrate the equation of the curve from x = 0 to the x-value where the parabola intersects the x-axis:
Area = ∫[0, x] (x^2) dx
Using the power rule of integration, we can integrate the equation:
Area = ∫[0, x] (x^2) dx = [x^3/3] from 0 to x
Area = (x^3/3) - (0^3/3) = x^3/3
Therefore, the area of the region bounded by the parabola y = x^2 is x^3/3.
To find the x-values where the curve intersects the x-axis, we set y = 0:
0 = x^2
x = 0
So, the parabola intersects the x-axis at x = 0.
To find the area bounded by the parabola, we integrate the equation of the curve from x = 0 to the x-value where the parabola intersects the x-axis:
Area = ∫[0, x] (x^2) dx
Using the power rule of integration, we can integrate the equation:
Area = ∫[0, x] (x^2) dx = [x^3/3] from 0 to x
Area = (x^3/3) - (0^3/3) = x^3/3
Therefore, the area of the region bounded by the parabola y = x^2 is x^3/3.
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The area of the region bounded by the parabola (y – 2)2 = x –1, the tangent of the parabola at the point (2, 3) and the x-axis is:a)6b)9c)12d)3Correct answer is option 'B'. Can you explain this answer?
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