The equation of the hyperbola whose foci are (6, 4) and (-4, 4) and eccentricity 2, is
Given: Foci are (6, 4) and (-4, 4) and eccentricity is 2
To find: equation of the hyperbola
Formula used:
Standard form of the equation of hyperbola is,
Center is the mid-point of two foci.
Distance between the foci is 2ae and b2 = a2(e2 – 1)
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)
Distance between the foci is 2ae and Foci are (6, 4) and (-4, 4)
{∵ e = 2}
b2 = a2(e2 – 1)
Equation of hyperbola:
Hence, required equation of hyperbola is