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The number of distinct normals that can be drawn from the point (0, 6) to the ellipse x2/169 + y2/25 = 1 is .....

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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.

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