Question

The focii of the parabolas $y^2=4x,x^2=4y,y^2+4x=0,x^2+4y=0$ taken in order will form the vertices of a

• A. rectangle
• B. parallelogram
• C. rhombus
• D. square

Answer 1

The correct option is D square

The focii of the parabolas $y^2=4x,x^2=4y,y^2+4x=0,x^2+4y=0$ will be $A(1,0),B(0,1),C(-1,0),D(0,-1)$ respectively.
On calculating, $AB,BC,CD,DA$, we get
$AB=BC=CD=DA=\sqrt{2}$
Also $AC=BD$
$\therefore$ It forms a square.