Question

If the line segment on Ix + my = n intercepted by the curve y${}^2$ = ax subtends a right angle at the origin, then

• A. $a,\sqrt{n},I$are in G.P
• B. $I,m,n$ are in G.P
• C. $l,m,n{}^2$ are in G.P
• D. 1, n${}^2$, m are in G.P

Answer 1

The correct option is A $a,\sqrt{n},I$are in G.P

$y^2=ax\left(\frac{lx+my}{n}\right)$ using Homoently

$\Rightarrow n{y}^2=al{x}^2+omxy$

For angle to ${90}^o$

$a+6=0$

$\Rightarrow -a+n=0$

$=n=al$

$a,\sqrt{n},\to GP$