Observe that y-axis is normal to the ellipse at (0, 5) and y-axis is passing through (0, 6). Now, a normal to the ellipse at (13 cos θ, 5 sin θ) is
13x/cosθ - 5x/sinθ = 169 - 25 = 144
This passes through the point (0, 6). So
-30/sinθ = 144
Hence, the number of normals that can pass through (0, 6) is 3.