Question

Question 17 O pts Write the equation of the parabola x2 + 2x +12y - 47 = o in standard form. Find the vertex, focus, directrix, axis of symmetry, and latus. Then graph and label your input on the graph.

Answer 1

x + 2x +127 - 47 = 0 → 2 x + 2x + 1 + 12 y -48 = 0 (+1) = -12 (4-4) (i) This is the standard form So the vertex is given by x+1= 0, y -4=0 vertex s (-1,4) Comaking i) with (x-2) = -40 (4-p) we get 49 = 12 a = 3 so focus is at Eri B-a)= (-1,4-3)=(-1,1) directrix is given by y = 8t a =4+3=7 axis of symmetry is given by 2+1 O 2 = -1 and the latus is the perpendicular to the axis of symmetry and passing through the foens so it is given by y= ß-a= 4-3 = 1 The graph is given below. y=7 dinectrix (-1/4) y=1 -20 -1D X=-4 axis of symmetry