Question

If x = a tan θ and y = b sec θ then

विकल्प

• ${\displaystyle \frac{y^2}{{\text{b}}^2}-\frac{x^2}{{\text{a}}^2}}$ = 1

• ${\displaystyle \frac{x^2}{{\text{a}}^2}-\frac{y^2}{{\text{b}}^2}}$ = 1

• ${\displaystyle \frac{x^2}{{\text{a}}^2}+\frac{y^2}{{\text{b}}^2}}$ = 1

• ${\displaystyle \frac{x^2}{{\text{a}}^2}-\frac{y^2}{{\text{b}}^2}}$ = 0

Answer 1

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

Explanation;

Hint:
x = a tan θ

${\displaystyle \frac{x}{\text{a}}}$ = tan θ

${\displaystyle \frac{x^2}{{\text{a}}^2}}$ = tan²θ

${\displaystyle \frac{y^2}{{\text{b}}^2}-\frac{x^2}{{\text{a}}^2}}$ = sec²θ – tan²θ = 1

y = b sec θ

${\displaystyle \frac{y}{\text{b}}}$ = sec θ

${\displaystyle \frac{y^2}{{\text{b}}^2}}$ = sec²θ