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The equation of the curve whose subnorma...

The equation of the curve whose subnormal is constant is

A

its eccentricity is 1

B

its eccentricity is `sqrt(2)`

C

its axis is the x-axis

D

its axis is the y-axis

Text Solution

Verified by Experts

The correct Answer is:
B
We have `y(dy)/(dx)=k` (constant)
or `ydy=kdx` or `y^(2)/2=kx+C` or `y^(2)=2kx+2C`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Multiple)
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  2. The differential equation whose solution is (x-h)^2+ (y-k)^2=a^2 is (a...

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  3. The equation of the curve satisfying the differential equation y((d...

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  4. Which of the following equation(s) is/are linear?

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  5. The solution of (dy)/(dx) = (ax + h)/(by + k) represents a parabola wh...

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  6. The equation of the curve satisfying the differential equation y2(x^2+...

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  7. Identify the statement(s) which is/are true.

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  8. The graph of the function y = f(x) passing through the point (0, 1) an...

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  9. If f(x), g(x) be twice differentiable functions on [0,2] satisfying f'...

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  10. The solution of the differential equation (x^2y^2-1)dy+2xy^3dx=0 is (a...

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  11. y=a e^(-1/x)+b is a solution of (dy)/(dx)=y/(x^2), then (a) ( b ...

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  12. The equation of the curve whose subnormal is constant is

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  13. The solution of (x d d+y dy)/(x dy-y dx)=sqrt((1-x^2-y^2)/(x^2+y^2)) i...

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  14. Find the curves for which the length of normal is equal to the radius ...

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  15. In which of the following differential equation degree is not defin...

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  16. If y=f(x) is the solution of equation ydx+dy=-e^(x)y^(2)dy, f(0)=1 and...

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  17. A particle falls in a medium whose resistance is propotional to the sq...

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