write an equation for the parabola with focus (1,3) and vertex (0,3)?

Question

a. y= 4(x-3)^2
b. y= -1/4(y+3)^2
c. y= -4(x+3/4)^2
d. y= 1/4(y-3)^2

Answer 1

The equation will be of the form x = (1/4a)(y-k)²+h
(h,k) is the vertex, a is determined from the focus coordinates.

x= (1/4a)(y-3)² + 0

a is the distance between the focus and vertex. It happens to be 1. a>0 if the focus is to the right of the vertex; a<0 if the focus is to the left.

This gives us x=(1/4)(y-3)²
D

Answer 2

you may not plug the concentration fee into equation, as some different person pronounced, on account that concentration isn't on the parabola. there's a formula to discover equation. enable vertex = (h, ok) and concentration = (h, ok+p) Vertex = (0, 0), concentration = (0, -5) = (0, 0.5) h = 0, ok = 0, p = -5 Equation of parabola: y - ok = a million/(4p) (x - h)² y - 0 = a million/(-20) (x - 0)² y = -a million/20 x² ==================== change technique: on account that concentration is 5 contraptions less than vertex, then directrix is 5 contraptions above vertex. Directrix has equation: y = 5 each and each element (x,y) on parabola is both distant to concentration and directrix. Distance from element (x,y) to concentration (0,-5) = ?(x² + (y+5)²) Distance from element (x,y) to directrix = ?(y-5)² on account that those distances are equivalent: ?(y-5)² = ?(x² + (y+5)²) (y-5)² = x² + (y+5)² y² - 10y + 25 = x² + y² + 10y + 25 - 10y = x² + 10y -20y = x² y = -a million/20 x²

Answer 3

Since the directrix is x = -1, by the definition of a parabola, a point on the curve is equidistant from the focus and the directrix, we have

(x-1)^2+(y-3)^2 = (x+1)^2

Simplify,
x^2-2x+1+(y-3)^2 = x^2-6x+1

Solve for x,
x = (1/4)(y-3)^2