Hello,

2(x-1)^2+2(y-1)^2=(x+y+2)^2

√ (x-1)^2+(y-1)^2 = |x+y+2/√1+1|

It represents a Parabola having

Focus at (1,1) &

Directrix is x+y+2=0

The equation of the axis is y-1=1(x-1)

i.e y= x

Y^2= 4ax

a=√2

So, y^2=4(√2)x

h=k, since(h,k) is a point on the axis of the parabola

Let the point be (x1,0)

For three distinct normal,

X1>2a= 2√2

Since |X1|= √h^2+k^2 = √2|h|

Hence, 2√2=h√2

h >2

Since the solution h>2 is not in the options that you have mentioned ,

The answer is option d none of these

Hope it helps