Bundle: Single Variable Calculus: Concepts And Contexts, 4th + Student Solutions Manual
4th Edition
ISBN: 9780495780595
Author: James Stewart
Publisher: Cengage Learning
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Question
Chapter T, Problem 2BDT
To determine
To find: The equation of the circle that has center at (−1,4) and passes through the point (3,−2).
Expert Solution & Answer
Answer to Problem 2BDT
The equation of the circle is (x+1)2+(y−4)2=52.
Explanation of Solution
Formula used:
The equation of the circle is (x−h)2+(y−k)2=r2, where the center of the circle is at the point (h,k), r is the radius of the circle.
Calculation:
Suppose, the equation of the circle is (x−h)2+(y−k)2=r2.
It is given that, the center of the circle is at the point (−1,4).
Thus, substitute h=−1 and k=4 in (x−h)2+(y−k)2=r2 to obtain the equation of the straight line,
(x+1)2+(y−4)2=r2
It is given that, the line passes through the point (2,−5).
Thus, the radius of the circle is the distance between the point (2,−5) and the radius. That is,
r2=(3−(−1))2+(−2−4)2=(4)2+(−6)2=16+36=52
Thus, substitute r2=52 in (x+1)2+(y−4)2=r2 to obtain the equation of the straight line,
(x+1)2+(y−4)2=52
Thus, the equation of the circle is (x+1)2+(y−4)2=52.
Chapter T Solutions
Bundle: Single Variable Calculus: Concepts And Contexts, 4th + Student Solutions Manual
Ch. T - Evaluate each expression without using a...Ch. T - Simplify each expression. Write your answer...Ch. T - Expand and simplify. (a) 3(x + 6) + 4(2x 5) (b)...Ch. T - Factor each expression. (a) 4x2 25 (b) 2x2 + 5x ...Ch. T - Simplify the rational expression. (a) x2+3x+2x2x2...Ch. T - Rationalize the expression and simplify. (a) 1052...Ch. T - Rewrite by completing the square. (a) x2 + x + 1...Ch. T - Solve the equation. (Find only the real...Ch. T - Solve each inequality. Write your answer using...Ch. T - State whether each equation is true or false. (a)...
Ch. T - Prob. 1BDTCh. T - Prob. 2BDTCh. T - Prob. 3BDTCh. T - Prob. 4BDTCh. T - Sketch the region in the xy-plane defined by the...Ch. T - FIGURE FOR PROBLEM 1 1. The graph of a function f...Ch. T - If f(x) = x3, evaluate the difference quotient...Ch. T - Find the domain of the function. (a)...Ch. T - How are graphs of the functions obtained from the...Ch. T - Without using a calculator, make a rough sketch of...Ch. T - Let f(x)={1x2ifx02x+1ifx0 (a) Evaluate f(2) and...Ch. T - If f(x) = x2 + 2x 1 and g(x) = 2x 3, find each...Ch. T - Prob. 1DDTCh. T - Prob. 2DDTCh. T - Find the length of an arc of a circle with radius...Ch. T - Prob. 4DDTCh. T - Express the lengths a and b in the figure in terms...Ch. T - If sinx=13 and secy=54, where x and y lie between...Ch. T - Prove the identities. (a) tan sin + cos = sec ...Ch. T - Find all values of x such that sin 2x = sin x and...Ch. T - Sketch the graph of the function y = 1 + sin 2x...
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