Question

One focus of a hyperbola is located at the point (1, –3) and the corresponding directrix is the line y = 2. Find the equation of the hyperbola if its eccentricity is 3/2. 

Answer 1

S(1 – 3) is the focus, equation of the directrix is y – 2 = 0 

P(x₁, y₁) is any point on the hyperbola join SP and draw PM 

perpendicular to the directrix S.P.= e.PM 

⇒ SP² = e².PM²

Focus of P(x₁,y₁) is 

4x² – 5y² – 8x + 60y + 4 = 0 

This is the equation of the required hyperbola