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The curve for which the slope of the tan...

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

Text Solution

Verified by Experts

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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NCERT EXEMPLAR-DIFFERENTIAL EQUATIONS -Differential Equations
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  8. The differential equation for which y=a cos x+b sin x is a solution is

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  9. The solution of (dy)/(dx)+y=e^(-x), y(0)=0 "is"

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  10. The order and degree of differential equation: ((d^(3)y)/(dx^(3)))^(...

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  11. The order and degree of differential equation: [1+((dy)/(dx))^(2)]=(d^...

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  14. The general solution of (dy)/(dx)+y tan x=sec x is

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  15. The solution of differential equation (dy)/(dx)+(y)/(x)=sin x is

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  16. The general solution of differential equation (dy)/(dx)=e^((x^(2))/(2)...

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  17. The solution of differential equation (dy)/(dx)=e^(x-y)+x^(2)e^(-y)is

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  18. The solution of differential equation (dy)/(dx)+(2xy)/(1+x^(2))=(1)/(1...

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  19. (i) The degree of the differential equation (d^(2)y)/(dx^(2))+e^(dy//d...

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