Give the equation of the hyperbola in standard form Please t

Give the equation of the hyperbola in standard form.

Please tell me the process in getting the answer. I want a step-by-step explanation of how the answer was derived. Thank you. The answer from the answer key is:

Solution

Eqn of hyperbola with axis along x-axis and center at (0,0) is (x^2/a^2) - (y^2/b^2)=1 => for axis along a line parallel to y-axis and center at (c,d) is ((y-d)^2/b^2)- ((x-c)^2/a^2)=1 axis is along x=0 (y-axis) center= (0,6) mid point of vertices => d=5, c=0 distance between center and vertex= b = 4 distance between center and focus= 6 = be => e=6/4=1.5 =>e= sqrt(1+(a^2/b^2)) =1.5 => a^2 = 1.25 * b^2 => a= sqrt(20) substitute these values in the above equation..u get the answer.. For more details about the properties, just lookup \'hyperbola\' in wiki..