Q. 85.0( 1 Vote )

Find the area common to the circle x2 + y2 = 16 a2 and the parabola y2 = 6ax.ORFind the area of the region {(x,y):y2 ≤ 6ax} and {(x,y):x2 + y2 ≤ 16a2}.  [CBSE 2013]

To find area given equations are

y2 = 6ax ...(i)

x2 + y2 = 16 a2 ...(ii)

On solving Equation (i) and (ii)

Or x2 + (6ax)2 = 16a2

Or x2 + (6ax)2 – 16a2 = 0

Or (x + 8a) (x – 2a) = 0

Or x = 2a or x = – 8a is not possible solution.

Then y2 = 6a(2a) = 12a2 = 2√3a

Equation (i) represents a parabola with vertex (0,0) and axis as x - axis.

Equation (ii) represents a with centre (0,0) and meets axes (±4a,0), (0,±4a).

Point of intersection of circle and parabola are (2a,2√3a), (2a, – 2√3a).

These are shown in the graph below: -

Required area = 2[Region ODCO + Region BCDB]

The area common to the circlex2 + y2 = 16 a2 and the parabola y2 = 6ax is

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Application of Biotechnology48 mins
Fundamental Integration Formula59 mins
Integration by Substitution56 mins
Interactive Quiz on Integration by Parts56 mins
Interactive Quiz on Integration by Substitution47 mins
Lecture on Integration by parts55 mins
Lecture on some forms of integration54 mins
Lecture on integration by partial fractions62 mins
How to find Maxima & Minima?43 mins
Tangent & Normal To A Curve53 mins
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