Application of DerivativeHard
Question
If tangents are drawn from the origin to the curve y = sin x, then their points of contact lie on the curve
Options
A.x - y = xy
B.x + y = xy
C.x2 - y2 = x2y2
D.x2 + y2 = x2y2
Solution
The tangent at (x1, sin x1) is y - sin x1 = cos x1 (x - x1)
It passes through the origin.
sin x1 = x1 cos x1 = x1
y12 = sin2 x1 = x12(1 - y12) ⇒ (x1y1) (x1y1) lies on the curve
y2 = x2(1 - y2).
⇒ x2 - y2 = x2y2
It passes through the origin.
sin x1 = x1 cos x1 = x1
y12 = sin2 x1 = x12(1 - y12) ⇒ (x1y1) (x1y1) lies on the curve
y2 = x2(1 - y2).
⇒ x2 - y2 = x2y2
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