SOLUTION: Please help me solve this equation: find an equation of the set of points such that each point satisfies the given conditions. -its distance from (0,-2) is 5

Question 901412: Please help me solve this equation:
find an equation of the set of points such that each point satisfies the given conditions.
-its distance from (0,-2) is 5
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

A point P(x,y) on an x-y plane at a distance of 5 units from (0,-2) will comply with
or
Maybe you are familiar with the formula on the left, which your teacher may have called "the distance formula".
Or maybe you realize that you can get the equation on the right by applying the Pythagorean theorem to right triangle CPQ above. (That is the basis of "the distance formula", anyway).
From the formulas above, you easily derive
as the equation for the set of points at a distance of 5 units from C(0,-2), which is the circle of radius 5, centered at C(0,-2).

MORE:
The equation above is the answer I like best, but it is not the only equation you can write. There are, of course, an infinite number of equivalent equations, most of them ridiculously and unnecessarily complicated.
--->---> gives you another reasonable option.
---> gives you another reasonable option.
--->---> ia an equivalent equation, made unnecessarily complicated by multiplying times 100.
We can multiply any equation times a non-zero number and get an equivalent equation.
RELATED QUESTIONS
please help me to solve this problem; given two points A and B such that l(AB)=6. Find... (answered by josgarithmetic)

Please help me solve this question Find an equation for the hyperbola that satisfies... (answered by lwsshak3)

Please help me solve this; Given are two points A(-1,3) and B(3,9).(a) Show that... (answered by KMST)

Find an equation for the set of points in an xy-plane that are equidistant from the point (answered by josgarithmetic)

Please Help!! Find an equation of the line that satisfies the given conditions Through (answered by CharlesG2)

Find an equation of the set of points on a plane such that the sum of the distances... (answered by ikleyn)

please help me find an equation for the ellipse that satisfies the given conditions.... (answered by lwsshak3)

Find an equation of the set of points in a plane such that the sum of distances between... (answered by josgarithmetic,ikleyn)

Could you please help me solve and understand this equation? Find an equation of the... (answered by ankor@dixie-net.com,jim_thompson5910)