ParabolaHard

Question

The area of the region bounded by the parabola (y - 2)2 = x - 1, the tangent to the parabola at the point (2, 3) and the x-axis is

Options

A.3
B.6
C.9
D.12

Solution

       
Equation of tangent at (2, 3) to
(y - 2)2 = x - 1 is S1 = 0
⇒     x - 2y + 4 = 0
Required Area = Area of ᐃOCB + Area of OAPD – Area of ᐃPCD
=
= 4 + - 1 = 4 - 9 - 18 + 15 - 1
= 28 - 19 = 9sq. units
    (or)
Area = (2y - 4 - y2 + 4y - 5)dy = (- y2 + 6y - 5)dy = - (3- y)2 dy = 9 sq.units

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