The length of the latus rectum of the parabol | vedclass

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(B) The focus of the parabola is $S = (1, -2)$.The equation of the directrix is $x + y + 3 = 0$.The distance from the focus to the directrix is denote

Vedclass · Accepted Answer

$2 \sqrt{2}$ units

Vedclass · Answer

(B) The focus of the parabola is $S = (1, -2)$.The equation of the directrix is $x + y + 3 = 0$.The distance from the focus to the directrix is denoted by $d$.The formula for the distance from a point $(x_1, y_1)$ to a line $ax + by + c = 0$ is $d = \frac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}$.Substituting the values,$d = \frac{|1(1) + 1(-2) + 3|}{\sqrt{1^2 + 1^2}} = \frac{|1 - 2 + 3|}{\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2}$.The length of the latus rectum of a parabola is $2 	imes (	ext{distance from focus to directrix})$.Length of latus rectum $= 2 	imes \sqrt{2} = 2 \sqrt{2}$ units.

The length of the latus rectum of the parabola whose focus is at $(1, -2)$ and directrix is the line $x + y + 3 = 0$ is

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