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Question

The focii of the parabolas y2=4x,x2=4y,y2+4x=0,x2+4y=0 taken in order will form the vertices of a

A
rectangle
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B
parallelogram
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C
rhombus
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D
square
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Solution

The correct option is D square
The focii of the parabolas y2=4x,x2=4y,y2+4x=0,x2+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=2
Also AC=BD
It forms a square.

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