The equation of the latus rectum of a parabol | vedclass

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(D) The distance between the tangent at the vertex $(x + y - 12 = 0)$ and the latus rectum $(x + y - 8 = 0)$ is equal to the distance $a$ between the

Vedclass · Accepted Answer

$8\sqrt{2}$

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(D) The distance between the tangent at the vertex $(x + y - 12 = 0)$ and the latus rectum $(x + y - 8 = 0)$ is equal to the distance $a$ between the vertex and the focus.Using the formula for the distance between two parallel lines $Ax + By + C_1 = 0$ and $Ax + By + C_2 = 0$,which is $d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}$:$a = \frac{|-12 - (-8)|}{\sqrt{1^2 + 1^2}} = \frac{|-4|}{\sqrt{2}} = \frac{4}{\sqrt{2}} = 2\sqrt{2}$.The length of the latus rectum is $4a$.Length $= 4 	imes (2\sqrt{2}) = 8\sqrt{2}$.

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

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