Question

If x=9 cos theta and y=40 sin theta ; eliminate theta

with all steps ​

Answer 1

Answer:

$Answer: \frac{ {x}^{2} }{81} + \frac{ {y}^{2} }{1600}$

Step-by-step explanation:

$x = 9 \cos\theta \: and \: y = 40 \sin\theta$

$\frac{x}{9} = \cos\theta \: \: (square \: both \: side)$

$\frac{ {x}^{2} }{81} = { \cos^{2} \theta} \: \: \:(eq1)$

similarly

$\frac{ {y}^{2} }{1600} = { \sin ^{2}\theta} \: \: \: \: (eq2)$

Add eq1 and eq2

$\frac{ {x}^{2} }{81} + \frac{ {y}^{2} }{1600} = { \sin}^{2} \theta + { \cos^2} \theta$

$\frac{ {x}^{2} }{81} + \frac{ {y}^{2} }{1600} = 1$

Thank you