Focus (2,−3), Directrix 3x−2y+5=0 Equation of parabola ‌(x−2)2+(y+3)2=‌
(3x−2y+5)2
32+22
⇒‌13x2−52x+52+13y2+78y+117 ‌‌=9x2+4y2+25−12xy−20y+30x ⇒‌4x2+12xy+9y2−82x+98y+144=0 ‌4x2+12xy+9y2=(2x+3y)2 Hence, they are two coincident lines.