ParabolaHardBloom L3
Question
The vertex of a parabola is at $(3,2)$ and its directrix is the line $x - y + 1 = 0$. Then the equation of its latus rectum is :
Options
A.$x - y = 2$
B.$x - y = 3$
C.$x - y = 1$
D.$x + y = 2$
Solution
Sol. [Key Concept: The latus rectum is the line through the focus parallel to the directrix; the focus is the vertex shifted along the axis by $a$ (the vertex–directrix distance).]
$$tan\theta = - 1 $$focus, $S \equiv \left( 3 - \sqrt{2}\left( - \frac{1}{\sqrt{2}} \right),2 - \sqrt{2}\left( \frac{1}{\sqrt{2}} \right) \right)$
$$S \equiv (4,1)$$
Eqn. of $LR \equiv x - y = 4 - 1 = 3$
$$x - y = 3$$
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