Find the equation of a parabola with focus (2, -3) and directrix x = 5.

Answer:The equation of the parabola is (y + 3)² = -6(x - 7/2)Step-by-step explanation:* Lets revise the equation of a parabola- If the equation is in the form (y − k)² = 4p(x − h), then: • Use the given equation to identify h and k for the vertex, (h , k) • Use the value of k to determine the axis of symmetry, y = k • Use h , k and p to find the coordinates of the focus, (h + p , k)• Use h and p to find the equation of the directrix, x = h − p* Now lets solve the problem∵ The directrix ⇒ x = 5∴ The form is (y − k)² = 4p(x − h)∵ The directrix is x = h - p∴ h - p = 5 ⇒ (1)∵ The focus is (h + p , k)∵ The focus is (2 , -3)∴ k = -3∴ h + p = 2 ⇒ (2)- Add (1) and (2) to find h∴ 2h = 7 ⇒ ÷ 2 for both sides∴ h = 7/2- Substitute this value in (1) or (2) to find p∴ 7/2 + p = 2 ⇒ subtract 7/2 from both sides∴ p = -3/2* Now we can write the equation∴ (y - -3)² = 4(-3/2) (x - 7/2)∴ (y + 3)² = -6(x - 7/2) ⇒ in standard form* The equation of the parabola is (y + 3)² = -6(x - 7/2)