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= x², y = x² −2x+2 7. Let a, b be fixed real numbers. Let P₁, P2 be parabolas with equations y = respectively. (a) Determine the unique point of intersection P of the parabolas P₁ and P₂. (b) Show that the line with equation y = ax + b is tangent to P₁, P2 if and only if a² = -4b, (a + 2)² = 4(2b) respectively. (c) Hence show that there is precisely one line L which is tangent to both P₁ and P2 and 1 show that its equation is y = x - (d) Determine the points of intersection Q, R of the line L with the parabolas P₁, P2 respectively. (e) Determine the area of the triangle PQR.

= x², y = x² −2x+2 7. Let a, b be fixed real numbers. Let P₁, P2 be parabolas with equations y = respectively. (a) Determine the unique point of intersection P of the parabolas P₁ and P₂. (b) Show that the line with equation y = ax + b is tangent to P₁, P2 if and only if a² = -4b, (a + 2)² = 4(2b) respectively. (c) Hence show that there is precisely one line L which is tangent to both P₁ and P2 and 1 show that its equation is y = x - (d) Determine the points of intersection Q, R of the line L with the parabolas P₁, P2 respectively. (e) Determine the area of the triangle PQR.

Calculus: Early Transcendentals
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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a, b be fixed real numbers. Let P₁, P2 be parabolas with equations y = x² = x², y = x² − 2x+2 respectively. (a) Determine the unique point of intersection P of the parabolas P₁ and P2. 7. Let (b) Show that the line with equation y = ax + b is tangent to P₁, P2 if and only if a² = −4b, (a + 2)² = 4(2 — b) respectively. (c) Hence show that there is precisely one line L which is tangent to both P₁ and P2 and show that its equation is y=x- 1 4* (d) Determine the points of intersection Q, R of the line L with the parabolas P1, P2 respectively. (e) Determine the area of the triangle PQR.
Transcribed Image Text:a, b be fixed real numbers. Let P₁, P2 be parabolas with equations y = x² = x², y = x² − 2x+2 respectively. (a) Determine the unique point of intersection P of the parabolas P₁ and P2. 7. Let (b) Show that the line with equation y = ax + b is tangent to P₁, P2 if and only if a² = −4b, (a + 2)² = 4(2 — b) respectively. (c) Hence show that there is precisely one line L which is tangent to both P₁ and P2 and show that its equation is y=x- 1 4* (d) Determine the points of intersection Q, R of the line L with the parabolas P1, P2 respectively. (e) Determine the area of the triangle PQR.
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