What is the equation of a parabola satisfying the given information? Focus (8, 2) directrix x= -9
2 Answers
Explanation:
Let (x0,y0) be any point on the parabola. Find the distance between (x0,y0) and the focus.
Then find the distance between (x0,y0) and directrix.
Equate these two distance equations and the simplified equation in x0 and y0 is equation of the parabola.
Equate the two distance expressions and square on both sides.
Explanation:
The distance from the focus,
The distance from the directrix,
Minus a minus is a plus:
Because a parabola is defined as the locus of points equidistant to its focus and its directrix, we set the right side of equation [1] equal to the right side of equation [2]:
Square both sides of the equation:
Expand the squares:
Combine like terms:
Write in the standard form:
This is a parabola that opens to the right:
graph{x = 1/34y^2-2/17y-13/34 [-19.23, 84.77, -21.25, 30.8]}