Find the equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y +3 = 0

Using the defination of parabola, we have

√((x – 2)² + (y – 3)²) = |x – 4y + 3| / √17

Squaring both sides:

⇒ 17(x² + y² – 4x – 6y + 13) = x² + 16y² + 9 – 8xy – 24y + 6x

Simplifying:

16x² + y² + 8xy – 74x – 78y + 212 = 0