Mathematics

Problem

The vertices of a hyperbola are

V_{1}(-6,0)

and

V_{2}(6,0)

, and its asymptotes are the straight lines

y=\frac{2}{3}x

and

y=-\frac{2}{3}x

. a. (i) Find the values of

a

and

b

for the hyperbola. b. (ii) Write its standard equation in simplest form. c. (iii) Calculate the coordinates of its foci. d. (iv) Sketch the hyperbola on suitable axes, showing and labelling the centre, vertices, foci, and asymptotes.

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