Question

Find the equation of the parabola whose focus is s(1, –7) and vertex is A(1, –2). 

Answer 1

Focus s = (1, -7), vertex A(1, –2)

h = 1, k = –2, a = –2 + 7 = 5 

since x coordinates of S and A are equal, axis of the parabola is parallel to y-axis. 

And the y coordinate of S is less than that of A, therefore the parabola is a down ward parabola. 

Let equation of the parabola be 

 (x – h)² = –4a(y – k) 

⇒ (x – 1)² = –20(y + 2) 

⇒ x² – 2x + 1 = –20y –40 

⇒x² – 2x + 20y + 41 = 0