Question

Find all the lines that pass through the point (1, 1) and are tangent to the curve represented parametrically as x = 2t t 2 and y = t + t2

Answer 1

The equation of the tangent is

y−(t+t2)x−(2t−t2)=1+2t2−2t

Now as it passes through (1,1)

1−(t+t2)1−(2t−t2)=1+2t2−2t

⟺2(1−t)(1−t−t2)=(1+2t)(1−t)2

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