The locus of a point moving under the condition that the line is a tangent to the hyperbola is
a circle
an ellipse
a hyperbola
a parabola.
As we learnt in
Condition for Tangency in Hyperbola -
- wherein
For the Hyperbola
is tangent to
Condition for tangency for y = mn + C is C2= a2m2 - b2
i.e.
Thus replace by (x, y)
y2 = a2x2 - b2 which is hyperbola.
Option 1)
a circle
this is incorrect option
Option 2)
an ellipse
this is incorrect option
Option 3)
a hyperbola
this is correct option
Option 4)
a parabola.
this is incorrect option
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