Eliminate '#theta#'?

Eliminate '#theta#' from the relations #5x = 3sectheta and y=3tantheta#.

1 Answer
Cesareo R.
Dec 9, 2017

#(5x)^2 + y^2=3^2#

Explanation:

#{(5x = 3/cos theta),(y=3sintheta/cos theta):}#

Dividing the second equation by the first

#y/(5x) = sin theta# and also #cos theta = 3/(5x)#

and now using the identity

#sin^2 theta+cos^2 theta = 1#

#(y/(5x))^2+(3/(5x))^2 = 1 rArr (5x)^2 + y^2=3^2#

which is the equation of an ellipse

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