Question

If h denote the A.M, k denote G.M of the intercepts made on axes by the lines passing through (1, 1) then (h, k) lies on

• A. $y^2=2x$
• B. $y^2=4x$
• C. $y=2x$
• D. $x+y=2xy$

Answer 1

The correct option is A $y^2=2x$

a = x - intercept, b = y - intercept
$2h=a+b,k^2=ab$
$\frac{x}{a}+\frac{y}{b}=1$​, substitute (1, 1)
$\frac{1}{a}+\frac{1}{b}=1$
a + b = ab
$2h=k^2\Rightarrow y^2=2x$