Question

Find the number of tangents to the curve y² – 2x² – 4y + 8 = 0, which pass through the point (1, 2).

Answer 1

Clearly, the point (1, 2) lies outside of the curve

y² – 2x² – 4y + 8 = 0.

(as 4 – 2 – 4 + 8 = 12 – 6 = 6 > 0)

Since the point lies outside of the given curve, so the number of tangent will be 2.