Answer :

Given: Vertices are (-8, -1) and (16, -1) and focus is (17, -1)


To find: equation of the hyperbola


Formula used:


The standard form of the equation of the hyperbola is,



Center is the mid-point of two vertices


The distance between two vertices is 2a


The distance between the foci and vertex is ae – a and b2 = a2(e2 – 1)


The distance between two points (m, n) and (a, b) is given by


Mid-point theorem:


Mid-point of two points (m, n) and (a, b) is given by



Center of hyperbola having vertices (-8, -1) and (16, -1) is given by




= (4, -1)


The distance between two vertices is 2a and vertices are (-8, -1) and (16, -1)







The distance between the foci and vertex is ae – a, Foci is (17, -1) and the vertex is (16, -1)








b2 = a2(e2 – 1)







The equation of hyperbola:






25(x2 + 16 – 8x) – 144(y2 + 1 + 2y) = 3600


25x2 + 400 – 200x – 144y2 – 144 – 288y – 3600 = 0


25x2 – 144y2 – 200x – 288y – 3344 = 0


Hence, required equation of hyperbola is 25x2 – 144y2 – 200x – 288y – 3344 = 0


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