The curve for which the slope of the tangent at any point is equal to the ration of the abcissa to the cordinates of the point is
The curve for which the slope of the tangent at any point is equal to the ration of the abcissa to the cordinates of the point is
A. an ellipse
B. parabola
C. circle
D. rectangular hyperbola
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Slope of tangent to the curve =`(dy)/(dx)`
and ratio of abscissa to the ordinate =`(x)/(y)`
According to the queston, `(dy)/(dx)=(x)/(y)`
`yd y=xdx`
On integrating both sides, we get
`(y^(2))/(2)=(x^(2))/(2)+C`
`Rightarrow (y^(2))/(2)-(x^(2))/(2)=C Rightarrow y^(2)-x^(2)=2C`
Which is an equation of reactangular hyperbola.
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