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Find the center of the circle(s) tangent to 5x – 2y – 1 = 0 at (1, 2) with a radius of 3. Express your answer as ordered pairs with coordinates rounded to the thousandths place, i.e. (3.123, 4.567). The x-component of the center of one circle is (_ ). A The y-component of the center of one circle is (_ The x-component of the center of the other circle is (---- A The y-component of the center of the other circle is ( v Hide hint for Question 3 Here you get two equations and two unknowns, since we know the center is at some point (h,k) the distance between that point and the point on the circle (1,2) is (1-h)2 + (2-K)2 = 32 We also know that the line containing the center of the circle is perpendicular to the tangent line. Thus using what we know from equations of lines we, that line's equation is y = -2/5x + 12/5 This gives us 2 equations and two unknowns. Since the first equation is squared, we know that we will get two solutions (Verify by drawing the picture).

Find the center of the circle(s) tangent to 5x – 2y – 1 = 0 at (1, 2) with a radius of 3. Express your answer as ordered pairs with coordinates rounded to the thousandths place, i.e. (3.123, 4.567). The x-component of the center of one circle is (_ ). A The y-component of the center of one circle is (_ The x-component of the center of the other circle is (---- A The y-component of the center of the other circle is ( v Hide hint for Question 3 Here you get two equations and two unknowns, since we know the center is at some point (h,k) the distance between that point and the point on the circle (1,2) is (1-h)2 + (2-K)2 = 32 We also know that the line containing the center of the circle is perpendicular to the tangent line. Thus using what we know from equations of lines we, that line's equation is y = -2/5x + 12/5 This gives us 2 equations and two unknowns. Since the first equation is squared, we know that we will get two solutions (Verify by drawing the picture).

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Find the center of the circle(s) tangent to 5x – 2y – 1 = 0 at (1, 2) with a radius of 3. Express your answer as ordered pairs with coordinates rounded to the thousandths place, i.e. (3.123, 4.567). The x-component of the center of one circle is (_ ). A The y-component of the center of one circle is (_ The x-component of the center of the other circle is (_. A The y-component of the center of the other circle is ( v Hide hint for Question 3 Here you get two equations and two unknowns, since we know the center is at some point (h,k) the distance between that point and the point on the circle (1,2) is (1-h)2 + (2-K)2 = 32 We also know that the line containing the center of the circle is perpendicular to the tangent line. Thus using what we know from equations of lines we, that line's equation is y = -2/5x + 12/5 This gives us 2 equations and two unknowns. Since the first equation is squared, we know that we will get two solutions (Verify by drawing the picture).
Transcribed Image Text:Find the center of the circle(s) tangent to 5x – 2y – 1 = 0 at (1, 2) with a radius of 3. Express your answer as ordered pairs with coordinates rounded to the thousandths place, i.e. (3.123, 4.567). The x-component of the center of one circle is (_ ). A The y-component of the center of one circle is (_ The x-component of the center of the other circle is (_. A The y-component of the center of the other circle is ( v Hide hint for Question 3 Here you get two equations and two unknowns, since we know the center is at some point (h,k) the distance between that point and the point on the circle (1,2) is (1-h)2 + (2-K)2 = 32 We also know that the line containing the center of the circle is perpendicular to the tangent line. Thus using what we know from equations of lines we, that line's equation is y = -2/5x + 12/5 This gives us 2 equations and two unknowns. Since the first equation is squared, we know that we will get two solutions (Verify by drawing the picture).
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