Sketch the region common to the cirvle `x^2+y^2=25` and the parabola `y^2=8x` Also find the area of the region using intergration .

Explanation

The given curves are
`x^2+y^2 =25`
and `y^2=8x`
On solving (i) and (ii) ,we get
`x^2+8x-25 =0 rArrx=(-8pmsqrt(64+100))/2 `
`rArr =-4pmsqrt(41)" "("rejecting -ve value ")`
Putting y=0 sin (i) we get `x= pm 5 `
Thus , the circle (i) cuts the x-axis at C(5,0) and C'(-5,0)
Required area = 2[area ODCAO]
=2 [(area ADCA )]
`=2(underset(0)overset(2)intsqrt(8x)" dx " +underset(a)overset(5)intsqrt(25-x^2)" dx ") " where "a=-4+sqrt(41)`