Question

Determine la ecuación general de la parábola con vértice en (3 ; −2 ) y cuya directriz es y = 5

Answer 1

Forma canónica:

$(x-h)^{2} =-4p(y-k)\\\\v (3 ; -2)\\\\(x-3)^{2} =-4p(y+2)\\\\p = 6\\\\(x-3)^{2} =-4(6)(y+2)\\\\\\\\(x-3)^{2} =-24y - 48\\\\(x)^{2}-6x+9 =-24y - 48\\\\(x)^{2}-6x+9+24y+48= 0\\\\(x)^{2}-6x+24y+55= 0$