In a coordinate problem a point is written as x = a \θ and y = b \θ , where a and b are non-zero constants. Eliminating \θ , which equation must x and y satisfy?

Question

Accepted Answer

x^2/a^2 - y^2/b^2 = 1. From the two equations, \θ = x/a and \θ = y/b . The identity that links this pair is ^2\θ - ^2\θ = 1 , giving x^2/a^2 - y^2/b^2 = 1 . Reaching for ^2 + ^2 = 1 out of habit produces the PLUS version, which belongs to x = a \θ,\ y = b \θ ; reversing the order of subtraction gives -1 , not +1 .

In a coordinate problem a point is written as $x = a sec θ$ and $y = b tan θ$ , where a and $b$ are non-zero constants.
Eliminating $θ$ , which equation must $x$ and $y$ satisfy?

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More Class 10 Trigonometric Identities practice

In a coordinate problem a point is written as x=asecθ and y=btanθ, where a and b are non-zero constants.Eliminating θ, which equation must x and y satisfy?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Trigonometric Identities practice

In a coordinate problem a point is written as $x = a sec θ$ and $y = b tan θ$ , where a and $b$ are non-zero constants.
Eliminating $θ$ , which equation must $x$ and $y$ satisfy?