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The family of curves, the subtangent at any point of which is the arithmetic mean of the coordinates of the point of tangency, is given by

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Find the family of curves, the subtangent at any point of which is the arithmetic mean of the co-ordinate point of tangency.

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Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

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For the curve y=a1n(x^2-a^2) , show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.

Family of curves whose tangent at a point with its intersection with the curve xy = c^2 form an angle of pi/4 is

The curve for which the slope of the tangent at any point is equal to the ration of the abcissa to the ordinate of the point is

Find the equation of all possible curves such that length of intercept made by any tangent on x-axis is equal to the square of X-coordinate of the point of tangency. Given that the curve passes through (2,1)

A conic passes through the point (2, 4) and is such that the segment of any of its tangents at any point contained between the co-ordinate axes is bisected at the point of tangency. Then the foci of the conic are:

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VMC MODULES ENGLISH-DIFFERENTIAL EQUATIONS-JEE ADVANCE (ARCHIVE )
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  3. The differential equation representing the family of curves y^2=2c(...

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  4. Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...

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  5. Prove that for x in [0, (pi)/(2)], sin x + 2x ge (3x(x + 1))/(pi).

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  6. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

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  7. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  8. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  9. Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2...

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  10. Consider the statements : P : There exists some x IR such that f(x)...

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  11. The function y=f(x) is the solution of the differential equation (d...

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  12. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

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  13. Let the f (x) be differentiabe function on the interval (0,oo) such ...

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  14. Integrating factor of sec^2y dy/dx+x tany=x^3

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  15. Let u(x) and v(x) be two continous functions satisfying the different...

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  16. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

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  17. A curve passes through the point (1,pi/6) . Let the slope of the curve...

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