If `h` denotes the A.M. and k denote G.M. of t e intercept made on axes by the lines passing through `(1, 1)` then `(h,k)` lies on

Options

A. `y^(2)=2x`
B. `y^(2)=4x`
C. `y = 2x`
D. `x +y = 2xy`

Answer

A

Explanation

Let x-intercept and y-intercept are a and b respectively.
Given `2h = a +b, k^(2) = ab`
Line with intercept a and b is `(x)/(a)+(y)/(b) =1`,
It passes through the point (1,1)
`:. (1)/(a)+(1)/(b) =1:. A+b = ab`
`:. 2h = k^(2)`
`:. y^(2) = 2x`