Question

Find the
area of the region bounded by
the Curves
y²= 2ax - x2 and y2°= ax
in the first quadrant ?


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Answer 1

Answer:

The answer

Step-by-step explanation

Solution :

x2+y2≤2ax

x2−2ax+y2+a2−a2≤0

(x−a)2+y2≤a2

y2≥ax

(x−a)2+ax=a2

x2+a2−2ax+ax=a2

x(x−a)=0

x=0,a

y2=ax

y2=a⋅a=a2

y=a

Area of region=∫2a0ydx

∫a0ax−−√dx+∫2aa2ax−x2−−−−−−−−√dx

a−−√∫a0x−−√dx+∫2aaa2−(x−a)−−−−−−−−−−√dx

23a2+[0+a2π4−0−0]

=23a2+π4a2

=a2(23+π4).