Question
The area (in sq. units) of the region
is
Solution
B.
Given equations of curves are
y2 = 2x ...(i)
which is a parabola with vertex (0,0) and parallel to X-axis and
x2 +y2 = 4x ... (ii)
which is a circle with centre (2,0) and radius = 2
on Substituting y2 = 2x in Eq (ii) we get
x2 + 2x = 4x
⇒ x2 +2x = 4x
⇒ x2 = 2x
⇒ x = 0 or x = 2
y =0 or y =±2 (using equ (i)]
Now, the required area is the area of shaded region, i.e,
y2 = 2x ...(i)
which is a parabola with vertex (0,0) and parallel to X-axis and
x2 +y2 = 4x ... (ii)
which is a circle with centre (2,0) and radius = 2
on Substituting y2 = 2x in Eq (ii) we get
x2 + 2x = 4x
⇒ x2 +2x = 4x
⇒ x2 = 2x
⇒ x = 0 or x = 2
y =0 or y =±2 (using equ (i)]
Now, the required area is the area of shaded region, i.e,
