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The slope of the tangent at (x , y) to a...

The slope of the tangent at `(x , y)` to a curve passing through a point `(2,1)` is `(x^2+y^2)/(2x y)` , then the equation of the curve is (a) `( b ) (c)2(( d ) (e) (f) x^(( g )2( h ))( i )-( j ) y^(( k )2( l ))( m ) (n))=3x (o)` (p) (b) `( q ) (r)2(( s ) (t) (u) x^(( v )2( w ))( x )-( y ) y^(( z )2( a a ))( b b ) (cc))=6y (dd)` (ee) (c) `( d ) (e) x(( f ) (g) (h) x^(( i )2( j ))( k )-( l ) y^(( m )2( n ))( o ) (p))=6( q )` (r) (d) `( s ) (t) x(( u ) (v) (w) x^(( x )2( y ))( z )+( a a ) y^(( b b )2( c c ))( d d ) (ee))=10 (ff)` (gg)

A

`x(x^(2) + y^(2)) = 10`

B

`x(x^(2) - y^(2)) = 6`

C

`2(x^(2) - y^(2)) = 6y`

D

`2(x^(2) - y^(2)) = 3x`

Text Solution

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The correct Answer is:
D
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AAKASH INSTITUTE ENGLISH-DIFFERENTIAL EQUATIONS-Assignment Section - B (Objective Type Questions (One option is correct))
  1. The differential equation (dy)/(dx)=(sqrt(1-y^2))/y determines a fa...

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  2. If y=y(x) and (2+sinx)/(y+1)((dy)/(dx))=-cosx ,y(0)=1, then y(pi/2)=

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  3. The slope of the tangent at (x , y) to a curve passing through a po...

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  4. The solution of the differential equation (dy)/(dx) = (y)/(x)+ (Q((...

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  5. The solution of differential equation x^(2)y^(2)dy = (1-xy^(3))dx is

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  6. Solve the following differential equation: (1+x^2)(dy)/(dx)+y=e^tan^((...

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  7. ydx+(x+x^(2)y)dy=0

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  8. The family whose x and y intercepts of a tangent at any point are resp...

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  9. The solution of the equation y' = cos (x-y) is

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  10. Solution of y dx – x dy = x^2 ydx is:

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  11. The equation of the curve, slope of whose tangent at any point (h, k) ...

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  12. Which of the following is a second order differential equation

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  13. The order of the differential equation whose general solution is y = (...

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  14. The equation of curve in which portion of y-axis cutoff between origin...

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  15. A curve y=f(x) passes through point P(1,1) . The normal to the curv...

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  16. Solve the following differential equation: tany(dy)/(dx)=sin(x+y)+sin(...

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  17. For solving dy/dx = 4x +y +1, suitable substitution is

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  18. A continuously differentiable function phi(x) in (0,pi) satisfying y'=...

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  19. Solve (1+e^(x/y))dx+e^(x/y)(1-x/y)dy=0

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  20. Order of the differential equation of the family of all concentric cir...

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