
How do you find the vertices, asymptotes, foci and graph ?
Answer
453.6k+ views
Hint: To get the vertices, asymptotes, foci and graph of the given equation, first of all we will modify the given equation in the standard form that will be the form of hyperbola. Then, we will use the different formulas for getting the values of vertices, asymptotes, foci and will draw the graph by using different values for variables.
Complete step by step answer:
Since, the given question is:
Now, we will convert it in the standard form of the hyperbola. So, we will divide in the given equation by both sides so that can get right hand side of the equation as:
Here, we will complete the division process by getting its quotient as:
Since, and are square of and respectively. So, we can write them below as:
Now, we will compare the obtained form of hyperbola with the standard form of hyperbola when its centre is , is . we will have:
and
Now, the vertex will be and when its centre is . So, we will put the value of and . Then, the vertex of the obtained hyperbola is:
and
Here, we will get the asymptotes with help of formula of asymptotes that is and . Now, we will apply the required values as:
and
and
And the foci of the hyperbola whose equation is , is and . Now, we will apply the value of the and in the foci and will get the foci of the hyperbola as:
and
and
Now, we do the necessary calculation as:
and
and
The graph of the hyperbola according to the obtained equation as will be as:
Hence, we got the final results related to the question.
Note: Here, I will write down all the formula to find vertices, asymptotes, foci and graph of hyperbola whose equation is , where is the centre of the hyperbola.
So, the vertices are and .
The asymptotes are and .
And the foci are and .
Complete step by step answer:
Since, the given question is:
Now, we will convert it in the standard form of the hyperbola. So, we will divide in the given equation by
Here, we will complete the division process by getting its quotient as:
Since,
Now, we will compare the obtained form of hyperbola with the standard form of hyperbola when its centre is
Now, the vertex will be
Here, we will get the asymptotes with help of formula of asymptotes that is
And the foci of the hyperbola whose equation is
Now, we do the necessary calculation as:
The graph of the hyperbola according to the obtained equation as

Hence, we got the final results related to the question.
Note: Here, I will write down all the formula to find vertices, asymptotes, foci and graph of hyperbola whose equation is
So, the vertices are
The asymptotes are
And the foci are
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