Answer
a) $k=1/4$;
b) $k=2$;
c) $k$ is any real number;
d) $k=4/3$.
Work Step by Step
In all of the parts we substitute for y the second coordinate of the point and for x the first coordinate of the point into the equation $y^2=4kx$ and then we calculate k.
a) $$1^2=4k\times 1\Rightarrow 1=4k\Rightarrow k=\frac{1}{4}$$
so for $k=1/4$ the graph passes through $(1,1)$.
b) $$4^2 = 4k\times2 \Rightarrow 16=8k\Rightarrow k=\frac{16}{8} = 2$$
so for $k=2$ the graph passes through $(2,4)$.
c) $$0^2 = 4k\times 0\Rightarrow 0=k\times 0.$$
The last equation is true for any real value of $k$ so for any $k\in \mathbb{R}$ the graph passes through $(0,0)$.
d) $$3^2 = 4k\times3 = \Rightarrow 9=12k\Rightarrow k=\frac{12}{9} =\frac{4}{3}$$
so for $k=4/3$ the graph passes through $(3,3)$.
