Q. 7 B

# Find the equation

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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