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Angle between Two Lines

The base of a...

Question

The base of a triangle lies along the line $x = a$ and is of length a. The area of the triangle is $a^{2} .$ The locus of the third vertex is

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Solution

Area $= a^{2}$
$\Rightarrow \frac{1}{2} \times a \times d = a^{2} \Rightarrow d = 2 a$
Perp. dist. $d = ∣ ∣ ∣ \frac{h (1) + k (0) - a}{\sqrt{1}} ∣ ∣ ∣$
$\Rightarrow 2 a = | h - a |$
$h + 3 a = 0$ or $h + a = 0$

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