Question

Equation of the conjugate axis of the hyperbola $5x^2-4y^2-30x-8y-39$ = 0

• A. x-3 = 0
• B. y+1 = 0
• C. x+3 = 0
• D. y-1 = 0

Answer 1

The correct option is A

x-3 = 0

$5x^2-4y^2-30x-8y-39=0$

$\Rightarrow$ $5(x^2-6x)-4(y^2+2y)=39$

$\Rightarrow$ 5 $(x-3{)}^2-4(y+1{)}^2=45-4+39$

$\Rightarrow$ $5(x-3{)}^2-4(y+1{)}^2=80$ $\Rightarrow$ $\frac{(x-3{)}^2}{16}-\frac{(y+1{)}^2}{20}$ = 1

Eq of conjugate axis x-3 = 0