Q. 275.0( 1 Vote )

Find the area of

Answer :

Given, A circle has equation 4x2 + 4y2 = 9 and a parabola x2 = 4y.

To Find: Find the area of a circle.


Explanation: We have a circle equation 4x2 + 4y2 = 9 and parabola x2 = 4y



We can write the given equation as



- - - - (i)


And, x2 = 4y - - - - (ii)


Now, Put the value of x2 in equation (i)





2y(2y + 9) - 1(2y + 9) = 0


(2y + 9)(2y - 1) = 0



Here, We neglect the negative value



Substitute the value of y in equation (ii)





Since,


Area of required region = 2 (Area in the first quadrant)








Hence, This is the required Area of given equation.


OR


Given, A triangle ABC , whose vertices are A(4, 1) , B(6, 6) and C(8, 4)


To Find: Find the area of triangle ABC using integration.


Explanation: We have three vertices of triangle A(4, 1) , B(6, 6) and C(8, 4).



Now, The equation of line AB is,





2y - 2 = 5x - 20


2y = 5x - 18



Now, The equation of BC is




y - 6 = - 1(x - 6)


BC = y = 12 - x


Similarly,


The equation of AC is





4y - 4 = 3x - 12



Area of ∆ABC = Area under AB + Area under BC – Area under AC







square units


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