Question

If a secФ =x and b tanФ =y , then how are x and y connected with a and b

Answer 1

secΦ=x/a tanΦ=y/b hence sec²Φ-tan²Φ=1=(x/a)²-(y/b)² Answer : (x/a)²-(y/b)²=1

Answer 2

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.