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  is negative, the parabola opens to the left.

Vertex .

Focus .

Graph:

Graph the and focus .

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Observe the graph:

The distance between focus and the point of tangency is .

is the one leg of the isosceles triangle.

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Substitute and .

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Find the point , the end point of the other leg of the isosceles triangle.

Since  is negative the parabola opens left and will be to the right of the focus.

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points and are the same point.

The slope between identical points is undefined.

The slope of tangent line is .

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Since the parabola opens horizontally and the slope of the tangent line is undefined, the line tangent to the graph at the vertex will be a vertical line.

Since the -coordinate of the vertex is , the equation for the line tangent to the parabola through this point is .

The tangent line equation is .

The tangent line equation is .