The parabola equation is and the point is
.
Since the square term is , the parabola is horizontal.
Standard form of the horizontal parabola is ,
where is vertex.
Focus .
\
The parabola equation .
Rewrite the equation as .
Compare the above equation with .
Since , the parabola opens right.
Vertex .
Focus .
The distance between focus and the point of tangency is .
\
Graph:
\Graph the and Focus
.
.
observe the graph:
\ is the one leg of the isosceles triangle.
.
Substitute and
.
.
\
Find the point , the end point of the other leg of the isosceles triangle.
Since is positive the parabola opens right and
will be to the left of the focus.
.
The tangent line passes through the points and
.
The slope of tangent line is .
.
The point-slope form of line equation is .
Substitute and
.
The tangent line equation is .
\
The tangent line equation is .