CONSIDER the curves y2=4x and x2=4y (i)the point of intersection of the curves are ` - Maths - Application of Integrals

Question

CONSIDER the curves y2=4x and x2=4y
​(i)the point of intersection of the curves are?? `
​(ii)using integration,find the area between the above two
curves
​

Varun.Rawat · Accepted Answer

The equation of the given curves are :y2 = 4x 1x2 = 4y 2The equation 1 represents a parabola having its vertex at the origin and axis along positive x-axis The equation 2 represents a parabola having its vertex at the origin and axis along positive y-axis POINTS OF INTERSECTION :From 2, we get y = x24Now, putting the value of y in 1, we getx416 = 4x⇒x4-64x = 0⇒xx3-64 = 0⇒x = 0 or x3 = 64⇒x = 0 or x = 4When x = 0; then y = 0When x = 4, then y = 4So, points of intersection of given curves are : 0,0 and 4,4

CONSIDER the curves y2=4x and x2=4y ​(i)the point of intersection of the curves are?? ` ​(ii)using integration,find the area between the above two curves ​

CONSIDER the curves y²=4x and x²=4y
(i)the point of intersection of the curves are?? `
(ii)using integration,find the area between the above two curves