The directrix of the equation is x=7
What is directrix of parabola?
The directrix of a parabola is a line that is perpendicular to the axis of the parabola. The directrix of the parabola helps in defining the parabola. A parabola represents the locus of a point which is equidistant from a fixed point called the focus and the fixed line called the directrix. The directrix and the focus are equidistant from the vertex of the parabola. Here we define the directrix for the standard equations of a parabola.
- The directrix of the parabola y^2 = 4ax, having x-axis as its axis, passes through (-a, 0), and has the equation x + a = 0.
- The directrix of the parabola y^2 = -4ax, having x-axis, passes through (a, 0), and has the equation x - a = 0.
- The directrix of the parabola x^2 = 4ay, having y-axis as its axis, passes through (0, -a), and has the equation y + a = 0.
- The focus of the parabola x^2 = -4ay, having y-axis as its axis, passes through (0, a), and has the equation y - a = 0.
Given:
-8(x-5)=(y+1)²
Now, using the definition of directrix
x= 8/4 +5
x= 2+ 5
x= 7
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