Precalculus 2014
47

 PAGE: 429 SET: Exercises PROBLEM: 47
Please look in your text book for this problem Statement

The parabola equation is and the point is .

Since the square term is , the parabola is vertical.

Standard form of the vertical parabola is ,

where is vertex.

Focus .

The parabola equation .

Compare the above equation with .

Since  is positive, the parabola opens up.

Vertex .

Focus .

Graph:

Graph the and Focus .

.

Observe the graph:

The distance between focus and the point of tangency is .

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 up and will be to the below 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 .

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