Explanation 1) Concept: Use the given information to find the equation of curve. 2) Calculation: Consider the isosceles triangle ∆ O P Q which is formed by the line drawn from the origin to any point x , y on the curve and extended tangent from that point which meet at x - axis. The side O P of a triangle is given by, O P = x - 0 2 + y - 0 2 = x 2 + y 2 = a 2 2 + y 2 = a 2 4 + y 2 From the figure, height of the triangle is h Here, O P = O Q Thus, by using Pythagoras rule, x 2 + y 2 = a 2 4 + h

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Author: James Stewart

Publisher: Cengage Learning

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Chapter 9.P, Problem 15P

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All curves with the property that if a line is drawn from the origin to any point x, y on the curve, and then a tangent is drawn to the curve at that point and extended to meet the x- axis, the result is an isosceles triangle with equal sides meeting at x, y.

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All curves with the property that if a line is drawn from the origin to any point x , y on the curve, and then a tangent is drawn to the curve at that point and extended to meet the x - axis, the result is an isosceles triangle with equal sides meeting at x , y .

Solution Summary: The author explains the isosceles triangle OPQ, which is formed by the line drawn from the origin to any point on the curve and extended tangent from that point.

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To find:

All curves with the property that if a line is drawn from the origin to any point x, y on the curve, and then a tangent is drawn to the curve at that point and extended to meet the x- axis, the result is an isosceles triangle with equal sides meeting at x, y.

Want to see the full answer?

Chapter 9 Solutions

All curves with the property that if a line is drawn from the origin to any point x , y on the curve, and then a tangent is drawn to the curve at that point and extended to meet the x - axis, the result is an isosceles triangle with equal sides meeting at x , y .

Solution Summary: The author explains the isosceles triangle OPQ, which is formed by the line drawn from the origin to any point on the curve and extended tangent from that point.

Videos

To find: All curves with the property that if a line is drawn from the origin to any point x, y on the curve, and then a tangent is drawn to the curve at that point and extended to meet the x- axis, the result is an isosceles triangle with equal sides meeting at x, y.

Want to see the full answer?

Chapter 9 Solutions

To find:

All curves with the property that if a line is drawn from the origin to any point x, y on the curve, and then a tangent is drawn to the curve at that point and extended to meet the x- axis, the result is an isosceles triangle with equal sides meeting at x, y.