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| PAGE: 429 | SET: Exercises | PROBLEM: 47 |
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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