Q. 7 A4.3( 4 Votes )

# Find the equation

Given: Foci are (6, 4) and (-4, 4) and eccentricity is 2

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 foci.

Distance between the foci is 2ae 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 foci (6, 4) and (-4, 4) is given by  = (1, 4)

The distance between the foci is 2ae, and Foci are (6, 4) and (-4, 4)      { e = 2}   b2 = a2(e2 – 1)    The equation of hyperbola:     12(x2 + 1 – 2x) – 4(y2 + 16 – 8y) = 75

12x2 + 12 – 24x – 4y2 – 64 + 32y – 75 = 0

12x2 – 4y2 – 24x + 32y – 127 = 0

Hence, required equation of hyperbola is 12x2 – 4y2 – 24x + 32y – 127 = 0

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