Q.

If the eccentricity of curve for which tangent at point P intersects the y axis at M above x-axis such  that origin is equidistant from M and point of tangency, is e, then value of 6e2 is

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answer is 6.

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Detailed Solution

We have OP=OM⇒y−xdydx=x2+y2⇒dydx=y−x2+y2x⇒dydx=yx−1+yx2 putting yx=v⇒dydx=v+xdvdx⇒v+xdvdx=v−1+v2⇒log⁡v+1+v2=log⁡cx⇒v+1+v2=cx⇒y+x2+y2=c ⇒curve is parabola ∴ e=1
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