First slide

Equation of line in Straight lines

Question

A stick of length $l$ moves on coordinate axes. The Locus of midpoint of the stick is

Moderate

A

$3 x^{2} + 3 y^{2} = l^{2}$
B

$4 x^{2} + 4 y^{2} = l^{2}$
C

$2 x^{2} + 2 y^{2} = l^{2}$
D

$x^{2} + y^{2} = l^{2}$

Solution

$L e t \frac{x}{a} + \frac{y}{b} = 1$ meets $x - a x i s$ at $A (a, 0)$
$y - a x i s$ at $B (o, b)$
$A B = l,$ $\Rightarrow a^{2} + b^{2} = l^{2}$ ___________(1)
Locus point $(x, y) = m i d p o int o f A B$
$(x, y) = (\frac{a}{2}, \frac{b}{2})$
$\Rightarrow a = 2 x, b = 2 y$
Substitute in (1) $\Rightarrow 4 x^{2} + 4 y^{2} = l^{2}$

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