Question

Find the equation of the parabola whose focus is (1,-7)S and vertex is T(1,-2)​

Answer 1

Question:

Find the equation of the parabola whose focus is (1,-7)S and vertex is T(1,-2)

Solution:

Since, the x-coordinate of S and T are same, the axis of the parabola is parallel to the x-axis and since the y-coordinate of T is greater than S, the parabola is downward type parabola.

Here, h= 1, k=-2 a=-2-(-7)=> 7-2=5

Let's the equation of the parabola be

$\tt (x-h)^2=-4a(y-k) \\\\ \to \tt (x-1)^2= -4(5)(y-(-2)) \\\\ \to \tt x^2+1-2x= - 20(y+2) \\\\ \to \tt x^2-2x+1=-20y-40 \\\\ \to \tt x^2-2x+20y+41=0$