Regarding parabola

Question

A point p on a parabola y² =4x, the foot from the perpendicular from it upon the directrix, and the focus of the parabola are the vertices of an equilateral triangle. If the area of the equilateral triangle is New. units. Then the value of N²/8 is equal to

Answer 1

points have names that are capital letters(e.g. P)

 

I take it that from P, on the parabola, a line segment is drawn ⊥ to the directrix.

F has coordinates (1,0) because little p = 1 for this parabola.

Let's call A the point on the directrix where this perpendicular from P line meets; then A is the third vertex of the equilateral triangle

 

 

The "foot from the perpendicular from it (P) upon the directrix" seems to be poor use of English.

 

It helps a lot to draw this parabola. Now you know the coordinates of the vertices of triangle FAP, which is equilateral; Does this give you enough information to compute the side lengths (they're all equal) using the distance formula? Area of equilateral triangle is ¼s²√3, of course, and this is to be called N?? (Another part of your detail is muddled).  Carry on!