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

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)

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 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
or
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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