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SecΦ=x/a tanΦ=y/b hence sec²Φ-tan²Φ=1=(x/a)²-(y/b)² Answer : (x/a)²-(y/b)²=1
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A secФ = x
⇒ sec Ф = x/a
b tanФ = y
⇒ tan Ф = y/b

we know that sec²Ф - tan²Ф = 1

 ( \frac{x}{a} )^{2} - (\frac{y}{b} )^{2} =1

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

This is an equation of hyperbola.
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