Find equations for the lines tangent and normal to the cissoid of Diocles y² (8-x) = 16x³ at (4,16). The equation of the line tangent to the curve at the point (4,16) is The equation of the line normal to the curve at the point (4,16) is (...) y² (8-x) = 16x³/ 16- (4,16) Q
Find equations for the lines tangent and normal to the cissoid of Diocles y² (8-x) = 16x³ at (4,16). The equation of the line tangent to the curve at the point (4,16) is The equation of the line normal to the curve at the point (4,16) is (...) y² (8-x) = 16x³/ 16- (4,16) Q
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Tangent and Normal Lines to the Cissoid of Diocles**
**Problem Statement:**
Find equations for the lines tangent and normal to the cissoid of Diocles given by the equation:
\[ y^2 (8 - x) = 16x^3 \]
at the point \((4, 16)\).
---
**Equations:**
1. The equation of the line tangent to the curve at the point \((4, 16)\) is \(\boxed{\phantom{entry}}\).
2. The equation of the line normal to the curve at the point \((4, 16)\) is \(\boxed{\phantom{entry}}\).
---
**Diagram Explanation:**
- The graph displayed shows a coordinate system with the x-axis and y-axis labeled.
- The cissoid of Diocles is graphed in blue and has a distinct curve.
- The point \((4, 16)\) is marked on the curve.
- Two lines are drawn:
- A red line represents the tangent to the curve at \((4, 16)\).
- A perpendicular line, presumably the normal, intersects the curve at the same point.
This visualization helps in understanding the orientation and position of the tangent and normal lines with respect to the curve at the specified point.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6f5a197-bd68-4fd1-8232-f49c284d6121%2F4e411f9b-c1ec-4158-80b3-a147ab69c966%2F5d8nn0r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Tangent and Normal Lines to the Cissoid of Diocles**
**Problem Statement:**
Find equations for the lines tangent and normal to the cissoid of Diocles given by the equation:
\[ y^2 (8 - x) = 16x^3 \]
at the point \((4, 16)\).
---
**Equations:**
1. The equation of the line tangent to the curve at the point \((4, 16)\) is \(\boxed{\phantom{entry}}\).
2. The equation of the line normal to the curve at the point \((4, 16)\) is \(\boxed{\phantom{entry}}\).
---
**Diagram Explanation:**
- The graph displayed shows a coordinate system with the x-axis and y-axis labeled.
- The cissoid of Diocles is graphed in blue and has a distinct curve.
- The point \((4, 16)\) is marked on the curve.
- Two lines are drawn:
- A red line represents the tangent to the curve at \((4, 16)\).
- A perpendicular line, presumably the normal, intersects the curve at the same point.
This visualization helps in understanding the orientation and position of the tangent and normal lines with respect to the curve at the specified point.
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