Question

Eliminate theta from x = 6 cosec theta and y = 8 sec theta​

Answer 1

Answer:

36

x

2

−

64

y

2

=1

Step-by-step explanation:

\text{Formula used:}Formula used:

cosec^2A-cot^2A=1cosec

2

A−cot

2

A=1

\text{Given:}Given:

x=6\:cosec\theta\:\text{and}\:y=8\:cot\thetax=6cosecθandy=8cotθ

\implies\:\frac{x}{6}=cosec\theta\:\text{and}\:\frac{y}{8}=cot\theta⟹

6

x

=cosecθand

8

y

=cotθ

\text{we know that}\:cosec^2\theta-cot^2\theta=1we know thatcosec

2

θ−cot

2

θ=1

\implies\:(\frac{x}{6})^2-(\frac{y}{8})^2=1⟹(

6

x

)

2

−(

8

y

)

2

=1

\implies\:\frac{x^2}{36}-\frac{y^2}{64}=1⟹

36

x

2

−

64

y

2

=1