Question

If x = a cos θ and y = b cot θ, show that: a^2/x^2 - b^2/y^2 = 1

Answer 1

$\underline\bold{\huge{ANSWER \: :}}$


GIVEN INFORMATIONS :

x = a cos theta

=> x/a = cos theta

=> a/x = sec theta

SIMILARLY, y = b cot theta

=> y/b = cot theta

=> b/y = tan theta


We know that,

sec²theta - tan²theta = 1

=> (a/x)² - (b/y)² = 1

=> a²/x² - b²/y² = 1 [SHOWED]

Answer 2

❤❤ HERE IS YOUR ANSWER ❤❤

______________________________

x = a cos theta

=> x/a = cos theta

=> a/x = sec theta

______________________________

y = b cot theta

=> y/b = cot theta

=> b/y = tan theta

______________________________


We already learn that,

sec²theta - tan²theta = 1

=> (a/x)² - (b/y)² = 1

=> a²/x² - b²/y² = 1 {Proved} ______________________________