MAT 121 Lecture Notes - Hypotenuse

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mathlover83

16 Jun 2022

School

Cairn University

Department

Mathematics

Course

MAT 121

Professor

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Document Summary

Circle: is the set of all points in a plane that lie a fixed distance from a fixed point. The fixed distance is called the radius and the fixed point is called the center of the circle: the equation of a circle centered at the origin. The simplest case is that of a circle whose center is at the origin. If we take any point (cid:1842)((cid:1876)(cid:481)(cid:1877)) on the circle, then (cid:1841)(cid:1842)(cid:3404)(cid:1870) is the radius of the circle. But (cid:1841)(cid:1842) is also the hypotenuse of the right-angled triangle (cid:1841)(cid:1842)(cid:1840), formed when we drop a perpendicular from (cid:1842) to the (cid:1876)-axis. Thus, using the theorem of pythagoras, (cid:1876)(cid:2870) (cid:3397) (cid:1877)(cid:2870) (cid:3404) (cid:1870)(cid:2870) (cid:481) and this is the equation of a circle of radius (cid:1870) whose center is the origin (cid:1841)((cid:882)(cid:481)(cid:882)). What is the equation of a circle of radius (cid:1870), centerd at the point (cid:6)((cid:131)(cid:481)(cid:132)): the general equation of a circle.

Related Questions

Use a pair of equations to describe the circle in which theplane through <1,1,3> perpendicular to the z-axis meetssphere of radius 5 centered at the origin.

Theequations:

So the circle on the xy plane is (x-1)^2+(y-1)^2 =? and z = 3

The sphere is x^2+y^2+z^2=25. What do I do to solve for theradius of the circle on the plane?