Mathematics

Mathematics

Problem

Find the length of the latus rectum of the parabola y2=4axy^{2}=4ax. a) 2a2a b) 4a4a c) aa d) 8a8a
Intuitive explanation

The latus rectum is the chord through the focus that's perpendicular to the parabola's axis of symmetry—it's a key "width" measurement that reveals how "open" or "tight" the parabola is. For y2=4axy^2 = 4ax, the focus lies on the xx-axis, so you just need to find where a vertical line through the focus intersects the parabola, then measure the distance between those two points.

Intuitive explanation

The latus rectum is the chord through the focus that's perpendicular to the parabola's axis of symmetry—it's a key "width" measurement that reveals how "open" or "tight" the parabola is. For y2=4axy^2 = 4ax, the focus lies on the xx-axis, so you just need to find where a vertical line through the focus intersects the parabola, then measure the distance between those two points.

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