The area (in square units ) of the triangle formed by y-axis , the straight line L passing through (1,1) and (2,0) and the straight line perpendicular to the line L and passing through (1/2, 0) , is

Options

A. 10 sq.units
B. `(11)/(3)" sq.units"`
C. `(25)/(16)" sq.units"`
D. `(20)/(3)" sq.units"`

Answer

C

Explanation

Let equation of line is `(x)/(a)+(y)/(b)=1`
`because` It is tangent of circle
`therefore (1)/(sqrt((1)/(a^(2))+(1)/(b^(2))))=sqrt(32)implies(1)/(a^(2))+(1)/(b^(2))=(1)/(32)`
`because G.M.geH.M.impliessqrt(a^(2)b^(2))ge(2)/((1)/(a^(2))+(1)/(b^(2)))`
`implies|ab|ge64impliesDeltaABCge64`