Tangent is drawn at the point `(x_(i), y_(i))` on the curve y = f(x), which intersects the x-axis at `(x_(i+1), 0)`. Now again tangent is drawn at `(x_(i+1), y_(i+1))` on the curve which intersects the x-axis at `(x_(i+2), 0)` and the process is repeated n times i.e. i = 1, 2, 3,......,n. If `x_(1), x_(2), x_(3),...,x_(n)` form a geometric progression with common ratio equal to 2 and the curve passes through (1, 2), then the curve isA. circleB. hyperbolaC. ellipseD. parabola

Tangent is drawn at the point `(x_(i), y_(i))` on the curve y = f(x),

1.	Tangent is drawn at the point `(x_(i), y_(i))` on the curve y = f(x), which intersects the x-axis at `(x_(i+1), 0)`. Now again tangent is drawn at `(x_(i+1), y_(i+1))` on the curve which intersects the x-axis at `(x_(i+2), 0)` and the process is repeated n times i.e. i = 1, 2, 3,......,n. If `x_(1), x_(2), x_(3),...,x_(n)` form a geometric progression with common ratio equal to 2 and the curve passes through (1, 2), then the curve isA. circleB. hyperbolaC. ellipseD. parabola
Answer» Correct Answer - B Again `x_(2) = x_(1) - (y_(1))/(((dy)/(dx)))` `because" "x_(1), x_(2), x_(3),.....x_(n)` are in G.P. `" "(x_(2))/(x_(1))=1-(y_(1))/(x_(1)((dy)/(dx)))` `rArr" "1-(y)/(x)(dx)/(dy)=2` `rArr" "-(y)/(x)(dx)/(dy)=1` `rArr" "(dx)/(x)=-(dy)/(y)` Integrating, `log x = - log y + log c` `rArr" "xy = c` Curve passing through `(1, 2)" "rArr" "c = 2` `therefore" "`Curve is xy = 2.

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