The equation of the latus rectum of a parabol | vedclass

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(D) The distance between the latus rectum and the tangent at the vertex of a parabola is equal to $a$, where $4a$ is the length of the latus rectum.Gi

Vedclass · Accepted Answer

$8 \sqrt{2} 	ext{ units}$

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(D) The distance between the latus rectum and the tangent at the vertex of a parabola is equal to $a$, where $4a$ is the length of the latus rectum.Given the equations $x+y-8=0$ and $x+y-12=0$.The distance $a$ between these two parallel lines is given by the formula $d = \frac{|c_1 - c_2|}{\sqrt{A^2 + B^2}}$.$a = \frac{|-8 - (-12)|}{\sqrt{1^2 + 1^2}} = \frac{4}{\sqrt{2}} = 2 \sqrt{2}$.The length of the latus rectum is $4a$.Length $= 4 	imes (2 \sqrt{2}) = 8 \sqrt{2} 	ext{ units}$.

The equation of the latus rectum of a parabola is $x+y=8$ and the equation of the tangent at the vertex is $x+y=12$. Then the length of the latus rectum is

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