# Let a and b be any two numbers satisfying Then,   the   foot   of perpendicular from the origin on the variable line, , lies on : Option 1) a hyperbola with each semi-axis = Option 2)  a hyperbola with each semi-axis = 2. Option 3)     a circle of radius = 2 Option 4)    a circle of radius =

As we learnt in

Equation of a line perpendicular to a given line -

is the line perpendicular to .

- wherein

is some other constant than.

Equation of line perpendicular to AB

ax - by = 0

Foot of perpendicular is

and ax - by = 0

Also,

Option 1)

a hyperbola with each semi-axis =

This is incorrect option

Option 2)

a hyperbola with each semi-axis = 2.

This is incorrect option

Option 3)

a circle of radius = 2

This is correct option

Option 4)

This is incorrect option

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