The area of the bounded region is .
The standard form of the hyperbola is where, is the major axis and is the minor axis.
The formula of is as follows:
The equation of the hyperbola is and the equation of the line is .
First we convert the given equation in the standard equation of hyperbola.
The given equation of hyperbola is .
Divide the given equation by .
Therefore, the given equation in the standard form of hyperbola is .
Now, we find the vertices of the hyperbola.
On comparing the given equation with standard form of hyperbola equation, We get
The vertices of the hyperbola is when major axis is the -axis.
Therefore, the vertices of the hyperbola is .
Now, sketch the graph of the hyperbola .
The vertices of the hyperbola is and the major axis is -axis.
Therefore, the graph can be drawn as in the attached Figure 1 (attached in the end).
The hyperbola is reflected about the -axis so the area below equals area above.
Therefore, the total area is double of the area of the region from to .
First we write the given equation of the hyperbola in terms of .
Now integrate the function with the limit from to as follows:
Further solve the above equation as follows:
The required area is the double of the above area.
Therefore, the area of the bounded region is .
1. Learn more about the function is graphed below brainly.com/question/9590016
2. Learn more about the symmetry for a function brainly.com/question/1286775
3. Learn more about midpoint of the segment brainly.com/question/3269852
Grade: High school
Chapter: Applications of derivatives
Keywords: Area, line, curve, limits, integration, bounded region, vertices, hyperbola, right side, reflected, function, anti-derivative, derivative, integral, shaded region, bounded area , interval.