The axis of a parabola is the line x+y=0, and its vertex and focus are in the first quadrant... --- *(reconstructed)* the focus is at (2,2) and the directrix is the line x+y=0. If the point (1,K) lies on the parabola, then a possible value of K is:
Solutions · 1
Official solution
Distance to directrix = distance to focus:
\[\frac{|1+K|}{\sqrt{2}}=\sqrt{(1-2)^2+(K-2)^2}.\]
\[(1+K)^2=2[1+(K-2)^2] \;\Rightarrow\; K^2-10K+9=0 \;\Rightarrow\; (K-9)(K-1)=0.\]
So K=9 (or 1).