Question

Eliminate theta from the equations x=a sec theta, y = b tan theta

Answer 1

this is your answer.

Answer 2

Note : Here I am using A instead of theta.

Given:

x = asecA

=> x/a = secA ----(1)

y = btanA

=> y/b = tanA -----(2)

We know the Trigonometric identity:

sec²A - tan²A = 1

=> (x/a)² - (y/b)² = 1

=> x²/a² - y²/b² = 1

Or

multiply each term by a²b² , we get

=> b²x² - a²y² = a²b²

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