The distance between the intersection point of the vertical line and the hyperbola and the two focal points can be obtained by making the x-axis vertical line between the hyperbola (xsquare) / 144 - (ysquare) / 25 = 1 and the focal point Through a focus of hyperbola (xsquare) / 144 - (ysquare) / 25 = 1, make a vertical line of X axis, and find the distance from the intersection of the vertical line and hyperbola to the two focuses A = 2x root 5, through the point a (- 5,2), the focus is on the X axis, find the standard equation of hyperbola

The distance between the intersection point of the vertical line and the hyperbola and the two focal points can be obtained by making the x-axis vertical line between the hyperbola (xsquare) / 144 - (ysquare) / 25 = 1 and the focal point Through a focus of hyperbola (xsquare) / 144 - (ysquare) / 25 = 1, make a vertical line of X axis, and find the distance from the intersection of the vertical line and hyperbola to the two focuses A = 2x root 5, through the point a (- 5,2), the focus is on the X axis, find the standard equation of hyperbola

X ^ 2 / 144-y ^ 2 / 25 = 1A = 12, B = 5C ^ 2 = a ^ 2 + B ^ 2 = 169c = 13 let (- 13,0) be a vertical line, x = - 13 be substituted into hyperbola 169 / 144-y ^ 2 / 25 = 1y ^ 2 = 625 / 144y = 25 / 12, y = - 25 / 144, so intersection (- 13,25 / 12), (- 13, - 25 / 12) then their distance to (- 13,0) = 25 / 12, from the definition of hyperbola to two