Q  If focus of a parabola is (2, 0) and one extremity of latus rectum is (2, 2),  then its equation is
(a) y² = 4 ( 3-x   )                (b) y² = 4x -4
(b) both (a) and (b)              (d) none of these

From the given information, It can be seen that the Letus Rectum is parallel to Y axis. that means tangent at vertex will also be parallel to X. that means, and focus is on X axis, therefore the vertex will also be on the X axis.

So the equation will be of the form: y2 = 4a(x- t), Now satisfy the point (2,2) and put a = 2, You will get the value of t from here.
$$\begin{gathered} 2^2=4\times 2\left(2-\mathrm{t}\right) \\ 1= 4-2\mathrm{t} \\ \mathrm{t} = \frac{3}{2} \\ \mathrm{so} {\mathrm{y}}^2=8\left(\mathrm{x}-\frac{3}{2}\right) \end{gathered}$$