# The normal to a curve at meets the axis at . If the distance of  from the origin is twice the abscissa of , then the curve is a Option 1) circle Option 2) hyperbola Option 3) ellipse Option 4) parabola

As we learnt in

Slope of a line -

- wherein

Slope of line joining A(x1,y1) and  B(x2,y2) .

If slope of tangent =

We get      as equation of normal.

If normal meets x-axis again, we get:

Distance of QG = 2 (abscissa of P)

i.e.,

Generalising

which is a Hyperbola.

Option 1)

circle

This option is incorrect.

Option 2)

hyperbola

This option is correct.

Option 3)

ellipse

This option is incorrect.

Option 4)

parabola

This option is incorrect.

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