15. Identify the equation of a parabola whose focus is at (5, -1) and whose directrix is x = 3.?

Question

A. x ^2 +2x – 4y +17= 0
B. x^2 – 2x – 4y +5 = 0
C. y^2 +2y – 4x +17= 0
D. y^2 – 2y – 4x +5 = 0

Answer 1

the vertex is equidistant from focus and directrix, so it's (4,-1). In addition, the parabola opens to the right, away from the directrix. The equation of a parabola that opens to the right is:

4p(x-h) = (y-k)²

where (h,k) is the vertex and p is the distance from vertex to focus (you make 4p positive or negative based on the direction it opens -- right or up, positive, left or down, negative). Since p = 1 in this parabola, the equation is,

4(x-4) = (y+1)² which is [c]

Answer 2

Steps: a million) Distribute on the two factors 2) combine like words on the two factors 3) circulate x variables to a minimum of one area, in many circumstances the left area 4) circulate non-x variables to the different area, in many circumstances the the best option area 5) divide the two factors via the x's optimal coefficient. 6) examine your artwork For the given situation: 5(x-a million) = 3(x+4) a million) 5x - 5 = 3x + 12 2) Already completed 3) 5x - 3x - 5 = 3x - 3x + 12 2x - 5 = 12 4) 2x - 5 + 5 = 12 + 5 2x = 17 5) 2x / 2 = 17 / 2 x = 17/2 6) Left area: 5(17/2 - a million) = 5(15/2) = 75/2 ** 17/2 - a million = 17/2 - 2/2 = 15/2 dazzling area: 3 (17/2 + 4) = 3(25/2) = 75/2 ** 17/2 + 4 = 17/2 + 8/2 = 25/2 the two factors are equivalent, consequently x = 17/2.

Answer 3

Using the definition
(x-5)^2+(y+1)^2=(x-3)^2
so
-10x+25+y^2+2y+1=-6x+9
4x=y^2+2y+17