+108 The hyperbola (y-3)^2/5 -(x-2)^2/16=1 (the equation is in x^2/a^2-y^2/b^2=1
Intersects the line at x=8 at (8,y1) and (8,y2) find y1+y2
+129850 (y - 3)^2 / 5 - (x - 2)^2 / 16 = 1
Since it intersects the line x = 8.....just sub this value of x into the equation
(y - 3)^2 / 5 - ( 8 -2)^2 / 16 = 1 simplify
Multiply through by the LCM of 5, 16 = 80
16 ( y - 3)^2 - 5 ( 8 - 2)^2 = 80 simplify
16 ( y -3)^2 - 5*6^2 = 80
16 ( y - 3) ^2 = 180 + 80
16 ( y - 3)^2 = 260 divide both sides by 16
(y - 3)^2 = 260/16 take both roots
y - 3 = sqrt ( 260/16) y = 3 + 2sqrt (65) /4 = 3 + sqrt (65) / 2 = y1
and
y - 3 = - sqrt (260/16) y = 3 - 2 sqrt (65) /4 = 3 - sqrt (65) /2 = y2
So
y1 + y2 = 6
