Concept explainers
The coordinates of the vertex, focus and the equation of directrix.
Answer to Problem 1RE
The coordinates of the vertex is
Explanation of Solution
The given equation is
It is of the standard form
The coordinates of the focus is
Find the value of
Therefore, the coordinates of the focus is
Standard equation of directrix is
Hence, for the given equation
Therefore the coordinate of the vertex is
To sketch: The parabola and its directrix for the equation
Explanation of Solution
Procedure used:
To sketch a parabola for an equation in the form
1. Write the given equation in the standard form
2. Calculate the value of
3. Plot the vertex at
4. The directrix
5. Substitute the
6. With vertex at
Calculation:
The given equation is
From the above part
Therefore, the coordinate of focus and equation of directrix are
Substitute the value of
Taking square root on both sides.
Therefore, the points are
The parabola and its directrix is sketched as follows:
From the above graph it is observed that
Whether the given equation is a function or not.
Answer to Problem 1RE
The given equation
Explanation of Solution
Procedure used:
To check whether the given equation is a function or not:
1. Plot the graph for the given equation.
2. For the resulting graph, apply the vertical line test.
3. Check whether the vertical line touches the parabola at only one point.
4. If the above condition is true, then the given equation is a function otherwise it is not a function.
Calculation:
The graph for the given equation is drawn as given below.
From the above figure it is observed that in the vertical line test the vertical line
Therefore, the equation
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Chapter D Solutions
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