The normal to a curve at `P(x , y)` meet the x-axis at `Gdot` If the distance of `G` from the origin is twice the abscissa of `P` , then the curve is a (a) parabola (b) circle (c) hyperbola (d) ellipse

Explanation

`(Y-y)=-dx/(dy)(X-x)`

`0-y=-(dx)/(dy)(G-x)`

`G=y(dy)/(dx)+x`

`|G|=2|x|`

`|x+(y)dy/(dx)|=2|x|`

`x+(y)dy/(dx)=2x or x+y(dy)/(dx)=-2x`

`y(dy)/(dx)=x or y(dy)/(dx)=-x`

`inty dy=intxdx or intydy=int-3xdx`

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