If the tangents at

Question

If the tangents at $P(1,1)$ on the curve $y^2 =x(2-x)^2$ meets the curve again at $Q$ then points of $Q$ is of the form $(3a/b,\, a/2b)$ so I have to find $a$ and $b$.

Answer 1

HINT:

First of all, $\left(\dfrac{3a}b,\dfrac a{2b}\right)$ lies on the given curve. This will give a relation between $a,b$

Find the equation of the tangent at $(1,1)$

Form the equation of the straight line joining $(1,1)$ and $\left(\dfrac{3a}b,\dfrac a{2b}\right)$

These two lines need to be the same

Optionally set $\dfrac ab=2t$ from the start