The point on the curve `sqrt(x) + sqrt(y) = sqrt(a)`, the normal at which is parallel to the x-axis, is

Options

A. (0,0)
B. (0,a)
C. (a,0)
D. (a,a)

Answer

B

Explanation

Since, equation of curve is ,brgt `sqrt(x)+sqrt(y)=sqrt(a)`.
`implies(1)/(2sqrt(x))+(1)/(2sqrt(y))(dy)/(dx)=0`
`implies(dy)/(dx)=-sqrt((y)/(x))`
Also, normal is parallel to X-axiis, then
`((dx)/(dy))_((x_(1),y_(1)))=0impliesx_(1)=0`
`thereforey_(1)=a`
hence, required point is (0,a).