Co-ordinates of the point on the curve x2+2xy+2y2=45 at which slope of tangent is -2,is/are ?(A) (3,0)(B)(-9,3)(C)(-3,1)(D)(9,-3)

Diifferentiating y w.r.t. x we get,2x + 2(y+ xdy/dx) + 4ydy/dx = 0dy/dx = -(x+y)/(x+2y) = -2on solving,x + 3y = 0orx = -3yput in the curve and solve we gety = + 3 and – 3and x = -9 and +9 respectively.Hence both are the solns.

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Grade 12th passDifferential Calculus

Co-ordinates of the point on the curve x²+2xy+2y²=45 at which slope of tangent is -2,is/are ?
(A) (3,0)
(B)(-9,3)
(C)(-3,1)
(D)(9,-3)

Pranav Dabhade

9 Years agoGrade 12th pass

1 Answer

Vikas TU

9 Years ago

Diifferentiating y w.r.t. x we get,

2x + 2(y+ xdy/dx) + 4ydy/dx = 0

dy/dx = -(x+y)/(x+2y) = -2

on solving,

x + 3y = 0

x = -3y

put in the curve and solve we get

y = + 3 and – 3

and x = -9 and +9 respectively.

Hence both are the solns.

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Co-ordinates of the point on the curve x2+2xy+2y2=45 at which slope of tangent is -2,is/are ?(A) (3,0)(B)(-9,3)(C)(-3,1)(D)(9,-3)

Pranav Dabhade

1 Answer

Vikas TU

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Co-ordinates of the point on the curve x²+2xy+2y²=45 at which slope of tangent is -2,is/are ?
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(B)(-9,3)
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