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CBSE Class 12 Math 2018 Solved Paper

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Question : 14 of 29
Marks: +1, -0
If (x2+y2)2 = xy, find
dy
dx
OR
If x = a (2θ - sin 2θ) and y = a (1 - cos 2θ) , find
dy
dx
 when θ =
π
3
Solution:  
(x2+y2)2 = xy
differentiating w.r.t. x
⇒ 2 (x2+y2) (2x+2y
dy
dx
) = y + x
dy
dx
⇒ 4x3+4x2yy
dy
dx
 + 4y2x + 4y3
dy
dx
 - y - x
dy
dx
 = 0
⇒ (4x2y+4y3−x)
dy
dx
 + 4x3+4y2x - y = 0
⇒ (4x2y+4y3−x)
dy
dx
 = - 4x3−4y2x + y
⇒
dy
dx
 =
−4x3−4y2x+y
4x2y+4y3−x
OR
x = a (2θ - sin 2θ)
y = a (1 - cos θ)
differentiating w.r.t. θ
dx
dθ
 = a (2 - cos 2θ × 2)
dy
dθ
 = a (+ sin 2θ × 2)
dy
dx
 =
(+sin2θ×2)
(−2cos2θ×2)
 =
(sin2θ)
(1−cos2θ)
dy
dx
 =
2sinθ×cosθ
2sin2θ
dy
dx
 =
cosθ
sinθ
 = cot θ
at , θ =
π
3
dy
dx
 = cot
π
3
 =
1
√3
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