Question

Equation of the hyperbola with focus (-3,4) directrix 3x-4y+5=0 and e = $\frac{5}{2}$ is

• A. $5x^2-24xy+12y^2+6x-8y-75=0$
• B. $5x^2-24xy+12y^2-8x-6y-25=0$
• C. $5x^2-24xy+12y^2-12x+8y-55=0$
• D. $5x^2-24xy+12y^2-7x-12y-65=0$

Answer 1

The correct option is A

$5x^2-24xy+12y^2+6x-8y-75=0$

S = ( -3,4) 3x - 4y + 5 = 0 $e=\frac{5}{2}$

$(x+3{)}^2+(y-4{)}^2=\frac{25}{4}\frac{(3x-4y+5{)}^2}{25}$

$\Rightarrow$ $4x^2+4y^2+24x-32y+100=9x^2+16y^2+25-24xy+30x-40y$

$\Rightarrow$ $5x^2-24xy+12y^2+6x-8y-75=0$