The equation of normal to the curve 2y=x² which passes through the point (2,1).
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Here, the curve is
2y = x² ...(i)
Now, differentiating both sides with respect to x, we get
2 dy/dx = 2x
⇒ dy/dx = x
⇒ - dx/dy = - 1/x
∴ (- dx/dy) at the point (2, 1) be
= - 1/2
∴ the required normal be
y - 1 = - 1/2 (x - 2)
⇒ 2 (y - 1) = - (x - 2)
⇒ 2y - 2 = - x + 2
⇒ x + 2y = 4
Hope it helps! (:
Here, the curve is
2y = x² ...(i)
Now, differentiating both sides with respect to x, we get
2 dy/dx = 2x
⇒ dy/dx = x
⇒ - dx/dy = - 1/x
∴ (- dx/dy) at the point (2, 1) be
= - 1/2
∴ the required normal be
y - 1 = - 1/2 (x - 2)
⇒ 2 (y - 1) = - (x - 2)
⇒ 2y - 2 = - x + 2
⇒ x + 2y = 4
Hope it helps! (:
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