Question

x=asec theta and y=btan theta .eliminate theta50 POINTS.answer correct.

Answer 1

x=asecø ,y = btanø .



secø=x/a

tanø =y/b

sec²ø-tan²ø=x²/a²-y²/b²

1=x²b²-y²a²/a²b²

a²b²=x²b²-y²a²

Hence theta is eliminated .I have used ø in place of ϴ

Answer 2

Given, x = a sec theta andy = b tan theta can be written as

         (x/a)  = sec theta  On squaring we get (x/a)^2 = sec^2 theta  ------ (1)

         (y/b)  =  tan theta  On squaring we get (y/b)^2 = tan^2 theta  ------ (2)


On subtracting equation (1) and (2), we get

x^2/a^2 - y^2/b^2 = sec^2 theta - tan^2 theta

x^2/a^2 - y^2/b^2 = 1    (sec^2 theta - tan^2 theta = 1)

x^2b^2 - y^2a^2/a^2b^2 = 1

x^2b^2 - y^2a^2 = a^2b^2.


Hope this helps!