The slope of the tangent to the curve at any point is the reciprocal o

1.	The slope of the tangent to the curve at any point is the reciprocal of four times the ordinate at that point. The curve passes through (2, 5). Find the equation of the curve.
Answer» Slope of the tangent is the reciprocal of four times the ordinate i.e., dy/dx = 1/4y 4∫y dy = ∫ dx 4(y²)/2 = x + c ⇒ 2y² = x + c Passes through (2, 5) ∴ c = 50 – 2 = 48 Equation of the curve is 2y² = x + 48

The slope of the tangent to the curve at any point is the reciprocal of four times the ordinate at that point. The curve passes through (2, 5). Find the equation of the curve.

Answer»

Slope of the tangent is the reciprocal of four times the ordinate

i.e., dy/dx = 1/4y

4∫y dy = ∫ dx

4(y²)/2 = x + c

⇒ 2y² = x + c

Passes through (2, 5)

∴ c = 50 – 2 = 48

Equation of the curve is 2y² = x + 48

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The slope of the tangent to the curve at any point is the reciprocal of four times the ordinate at that point. The curve passes through (2, 5). Find the equation of the curve.

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