Q. 285.0( 3 Votes )

Using integration

Answer :

Plotting the points, we get,

Let us first find the equation of sides of the triangle,

Equation of line passing from points P(x1, y1) and Q(x2, y2) is given by:


Equation of AB:

y – 5 = (x – 2)

y = x + 3

Equation of BC:

Equation of AC:

Now, let us look at the limits that we have to take,


Area = 21 square units.


Given Curves: C1: x2 + y2 = 8x

C2: y2 = 4x

Let us find the intersection point of the curves.

Putting the value of y2 from second curve in first curve,

x2 + 4x = 8x

x2 – 4x = 0

x(x – 4) = 0

x = 0 or x = 4


y2 = 4.0, y = 0

y2 = 4.4, y = ± 4

On plotting we will get,

Area required is shared in the given figure,

Area required will be found by:


Area required = Area OPC + Area PCQ

For parabola, y = ±√4x

y = ±2√x

Area OPC

Now, for circle,

Area of PCQ

Now, we know that,


Area PCQ

= 4π

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