Question

A ladder $12units$ long slides in a vertical plane with its ends in contact with a vertical wall and a horizontal floor along x-axis. The locus of a point on the ladder 4 units from its one end has the equation :

• A. $\frac{x^2}{4}+y^2=1$
• B. $\frac{x^2}{16}+\frac{y^2}{64}=1$
• C. $\frac{x^2}{64}+\frac{y^2}{16}=1$
• D. $x^2+\frac{y^2}{4}=1$

Answer 1

The correct option is C $\frac{x^2}{64}+\frac{y^2}{16}=1$

Given the length of ladder $=12units=S$

The locus of a point on the ladder $=4units=K$

The equation of the locus of a point from one end

$\frac{x^2}{(S-K{)}^2}+\frac{y^2}{K^2}=1\Rightarrow \frac{x^2}{(12-4{)}^2}+\frac{y^2}{4^2}=1\frac{x^2}{64}+\frac{y^2}{16}=1$