Question

Length of the lactus rectum of the elips presented by x=3(cos t+sin t) . Y=4(cos t-sin t) is given by

Answer 1

i) From the given data, we have x/3 = cos(t) + sin(t) and y/4 = cos(t) - sin(t)

ii) Squaring them and adding, x²/9 + y²/16 = 1

This is of the form x²/b² + y²/a² = 1, with a > b.

This ellipse center is (0, 0) and major axis along y-axis. b = 3 and a = 4; eccentricity e = √7/4

Parametric form of any point on this is (3cos(t), 4sin(t))

iii) Length of latus rectum = 2b²/a = 2*9/4 = 9/2 = 4.5 units.

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Answer 2

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