Question

if x=asec theta , y=atan theta then eliminate theta​

Answer 1

Step-by-step explanation:

$\frac{ {x}^{2} }{ {a}^{2} } = {sec}^{2} theta$

$\frac{ {y}^{2} }{ {a}^{2} } = {tan}^{2} theeta$

Subtracting both equations

$\frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {a}^{2} } = {sec}^{2} theta \: - {tan}^{2} theeta$

Put

${tan}^{2} theta = {sec}^{2} theta - 1$

We get theta free equation

$\frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {a}^{2} } = 1$