the tangent line to a certain curve at any point p(x, y) has an x-intercept equal to 3 4 x. this curve also passes through the point (1, 16). find the equation of this curve.

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09-12-2022
Mathematics

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the tangent line to a certain curve at any point p(x, y) has an x-intercept equal to 3 4 x. this curve also passes through the point (1, 16). find the equation of this curve.

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-17T07:37:31-05:00

At any point p(x, y), the tangent line to a particular curve has an x-intercept of 3 4 x. The point is also traversed by this curve (1, 16). The equation of the curve is y - 16 = (3/4)(x - 1)^2

To find the equation of the curve, we first need to find the equation of the tangent line at point P(x, y).

Since the x-intercept is 3/4x, the equation of the tangent line is

y - y_p = (3/4)(x - x_p).

We substitute the given point (1, 16) in the equation to find the value of y_p and x_p which are 16 and 1 respectively.

y - 16

= (3/4)(x - 1).

This equation is the equation of the curve.

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