It is known that the focal length of ellipse C equation is 4 and the equation of solving ellipse through P [√ 2, √ 3]

It is known that the focal length of ellipse C equation is 4 and the equation of solving ellipse through P [√ 2, √ 3]

Let the standard equation of the ellipse be: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 factor, focal length = 4, that is, 2C = 4, C = 2, C ^ 2 = a ^ 2-B ^ 2 = 2 ^ 2, so a ^ 2-B ^ 2 = 4 --- (1) factor, ellipse passes through P [(2 / 3) * root sign, (- 2 / 3) * root sign 6] and substituting the coordinates of P point into the standard equation of the ellipse, we get: {[(2 / 3) * root sign 6] ^ 2 / A ^ 2} + {[(- 2 / 3) *