+125 The line 2y=3x intersects the ellipse \(\frac{x^2}{8} + \frac{y^2}{18} = 1\) at the points \(Q\) and \(R\), what is the length of segment QR?
ty 
+23252 2y = 3x ---> y = (3/2)x
x2 / 8 + y2 / 18 = 1 ---> x2 / 8 + [(3/2) x ]2 / 18 = 1
---> x2 / 8 + (9/4) x2 / 18 = 1
---> x2 / 8 + 9 x2 / 72 = 1
---> 9 x2 + 9 x2 = 72
---> 18 x2 = 72
---> x2 = 4
---> x = 2 ---> y = 3 ---> (2, 3)
---> x = -2 ---> y = -3 ---> (-2, -3)
Now, use the distance formula to find the distance between these two points.
