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How do you find the vertices, asymptotes, foci and graph 100x281y2=8100 ?

Answer
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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 x2a2y2b2=1 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:
100x281y2=8100
Now, we will convert it in the standard form of the hyperbola. So, we will divide in the given equation by 8100 both sides so that can get 1 right hand side of the equation as:
100x2810081y28100=81008100
Here, we will complete the division process by getting its quotient as:
x281y2100=1
Since, 81 and 100 are square of 9 and 10 respectively. So, we can write them below as:
x292y2102=1
Now, we will compare the obtained form of hyperbola with the standard form of hyperbola when its centre is (0,0) , is x2a2y2b2=1 . we will have:
a=9 and b=10
Now, the vertex will be (a,0) and (a,0) when its centre is (0,0) . So, we will put the value of a and b. Then, the vertex of the obtained hyperbola is:
(9,0) and (9,0)
Here, we will get the asymptotes with help of formula of asymptotes that is y=bax and y=bax . Now, we will apply the required values as:
y=bax and y=bax
y=109x and y=109x
And the foci of the hyperbola whose equation is x2a2y2b2=1 , is (a2+b2,0) and (a2+b2,0) . Now, we will apply the value of the a and b in the foci and will get the foci of the hyperbola x292y2102=1 as:
(a2+b2,0) and (a2+b2,0)
(92+102,0) and (92+102,0)
Now, we do the necessary calculation as:
(81+100,0) and (81+100,0)
(181,0) and (181,0)
The graph of the hyperbola according to the obtained equation as x292y2102=1 will be as:
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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 (xh)2a2(yk)2b2=1 , where (h,k) is the centre of the hyperbola.
So, the vertices are (h+a,k) and (ha,k) .
The asymptotes are y=ba(xh)+k and y=ba(xh)+k .
And the foci are (h+a2+b2,k) and (ha2+b2,k) .