Answer:
x = 1/20 y^2
Step-by-step explanation:
This is a rightward opening (sideways ) parabola
Directrix = x = -5
Distance formula form point x,y to directrix and focus are equal:
(x - -5)^2 = (x-5)^2 + y^2
x^2 + 10x + 25 = x^2 - 10x + 25 + y^2
20x = y^2
x = 1/20 y^2
Find plane Π parallel to 5y-5x-5z=4 containing point p=(2,3,4)
Any plane parallel to 5y-5x-5z=4 has the form 5y-5x-5z=k, or on simplification, y-x-z=k.
Since p lies in the plane, the coordinates of p must satisfy y-x-z=k, or
k=3-2-4=-3
=>
π : y-x-z=-3
equivalently,
π : 5y-5x-5z=-15