# Find the area of

Given the boundaries of the area O befound are,

• Curve is y2 = 2y – x

• Y-axis.

Consider the curve, y2 = 2y –x

y2 – 2y = -x

by adding 1 on both sides

y2 – 2y + 1 = -(x-1)

(y-1)2 = -(x-1)

From the above equation, we can say that, the given equation is that of a parabola with vertex at A(1,1)

Consider the line x = 0 which is the y-axis, now substituting x = 0 in the curve equation we get

y2- 2y = 0

y(y-2)=0

y = 0 (or)y = 2

So , the parabola meets the y-axis at 2 points, B (0,2) and •(0,0) As per the given boundaries,

• The parabola y2 = 2y-x, with vertex at A(1,1).

• X= 0 which is the y-axis.

The boundaries of the region to be found are,

Point A, where the curve y2 = 2y-x has the extreme end the vertex i.e. A (1,1)

Point O, which is the origin

Point B, where the curve y2 = 2y-x and the y – axis meet i.e. B (0,2)

Consider the curve,

y2 = 2y - x

x = 2y - y2

Area of the required region = Area of OBAO.   [Using the formula ] The Area of the required region Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Find the area of Mathematics - Board Papers

Sketch the graph Mathematics - Board Papers

Using integrationMathematics - Board Papers

Find the area of Mathematics - Board Papers