The graph of the given equation is hyperbola.
Consider the equation:
25[tex] x^{2} [/tex] - 16[tex] y^{2} [/tex] = 400
⇒ [tex] \frac{25}{400} x^{2} [/tex] - [tex] \frac{16}{400} y^{2} [/tex] = [tex] \frac{400}{400} [/tex]
⇒ [tex] \frac{ x^{2} }{16} [/tex] - [tex] \frac{ y^{2} }{25} [/tex] = 1
This equation is of the form of hyperbola with center (0,0) and vertices (4,0) and (-4,0).
The graph of the hyperbola is given below:
