Question

The equation of the parabola with focus (a, b) and directrix $\frac{x}{a} + \frac{y}{b} = 1$ is given by

• A. (ax – by)² – 2a³x – 2b³y + a⁴ + a²b² + b⁴ =0
• B. (ax + by)² – 2a³x – 2b³y – a⁴ + a²b² – b⁴ =0
• C. (ax – by)² + a⁴ + b⁴ – 2a³x = 0
• D. (ax – by)² – 2a³x =0

Answer 1

Answer: (A)

(ax – by)² – 2a³x – 2b³y + a⁴ + a²b² + b⁴ =0

Answer 2

(x – a)² + (y-b)² = $\left( \frac{bx + ay - ab}{\sqrt{a^{2} + b^{2}}} \right)^{2}$

On solving we get

(ax – by)² – 2a³x – 2b³y + a⁴ + a²b² + b⁴ =0