6. Find all points with second coordinate -3 that are 6 units from (3, 2). 7. Find the equation of the circle with center (2, -4) and tangent to the y- axis. 8. Find the equation of the circle with center (-9, -3) and tangent to the x- axis. 9. Find the equation of the circle such that the endpoints of a diameter are (-2, 8) and (8, -6). 10.Find the perimeter and area of the right triangle with vertices (1,2), (5,5), and (-2, 6).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Worksheet 6.1: The Coordinate Plane,
Equations of Circles, and the Distance and Midpoint Formulas
For each problem below, use algebra to answer the questions. You may
find
it helpful to draw and label an appropriate picture to help you get started and
verify that your answer is reasonable. (Even if you are quite sure you can
answer the question from your picture alone, you must use algebra to justify
your answer.)
Transcribed Image Text:Worksheet 6.1: The Coordinate Plane, Equations of Circles, and the Distance and Midpoint Formulas For each problem below, use algebra to answer the questions. You may find it helpful to draw and label an appropriate picture to help you get started and verify that your answer is reasonable. (Even if you are quite sure you can answer the question from your picture alone, you must use algebra to justify your answer.)
6. Find all points with second coordinate -3 that are 6 units from (3, 2).
7. Find the equation of the circle with center (2, -4) and tangent to the y-
axis.
8. Find the equation of the circle with center (-9, -3) and tangent to the x-
axis.
9. Find the equation of the circle such that the endpoints of a diameter
are (-2, 8) and (8, -6).
10. Find the perimeter and area of the right triangle with vertices (1,2),
(5,5), and (-2, 6).
Transcribed Image Text:6. Find all points with second coordinate -3 that are 6 units from (3, 2). 7. Find the equation of the circle with center (2, -4) and tangent to the y- axis. 8. Find the equation of the circle with center (-9, -3) and tangent to the x- axis. 9. Find the equation of the circle such that the endpoints of a diameter are (-2, 8) and (8, -6). 10. Find the perimeter and area of the right triangle with vertices (1,2), (5,5), and (-2, 6).
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