Question

Tangents are drawn to the hyperbola $3x^2-2y^2=25$ from the point $(0,\frac{5}{2})$. Find their equations.

• A. $2x+3y-\frac{15}{2}=0;2x-3y+\frac{15}{2}=0$
• B. $2x+3y-\frac{15}{2}=0;3x-2y+5=0$
• C. $3x+2y-5=0;2x-3y+\frac{15}{2}=0$
• D. $3x+2y-5=0;3x-2y+5=0$

Answer 1

The correct option is D $3x+2y-5=0;3x-2y+5=0$

Tangent to the hyperbola is given by $y=mx\pm \sqrt{a^2{m}^2-b^2}$
Since, it passes through $(0,\frac{5}{2})$
Therefore, $\frac{5}{2}=\sqrt{\frac{25m^2}{3}-\frac{25}{2}}$
$\Rightarrow m=\frac{\pm 3}{2}$