A parabola has a vertex at the origin. The equation of the directrix of the parabola is y = 3. What are the coordinates of its focus?(0,3)(3,0)(0,–3)(–3,0)URGENT. NEED HELP QUICK.
Accepted Solution
A:
Answer:The correct option is 3.Step-by-step explanation:The vertex of parabola is origin and directrix of the parabola is y = 3.The standard form of a parabola is[tex](x-h)^2=4p(y+k)[/tex]Where (h,k) is vertex. (h,k+p) is focus and y=k-p is directix.The vertex of parabola is origin. So,[tex]h=0[/tex][tex]k=0[/tex]Directrix of the parabola is y = 3.[tex]y=k-p[/tex][tex]3=0-p[/tex][tex]-3=p[/tex]The value of p is -3.Focus of the parabola is (h,k+p).[tex](h,k+p)=(0,0-3)[/tex][tex](h,k+p)=(0,-3)[/tex]Therefore focus of the parabola is (0,-3) and option 3 is correct.