Show that the point P (4, -5) lies on the circle with center (4,-1) and radius 4root2?

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answers:
no sea nabo say: center (a,b) radius =r
so
(x–a)² + (y–b)² = r²
(x-4)² + (y+1)² = (4√2)²
x²+y²-8x+2y+17=32
x²+y²-8x+2y-15=0
for (4,-5)
(4)²+(-5)²-8(4)+2(-5)+17=0
16+25-32-10-15=0
-16=0 FALSE
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Puzzling say: It's pretty easy to see the distance between the point (4,-5) and the center (4,-1) is *4* units. The x-coordinates are the same so we only have to find the distance between the y-coordinates by subtracting.

If the distance is 4, it can't be 4√2.

Double-check your question for a mistake. My guess is that one of the x-coordinates was either 0 or 8.
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billrussell42 say: Show that the point P (4, -5) lies on the circle with center (4,-1) and radius 4root2?

equation of circle with center at a,b and radius r
(x–a)² + (y–b)² = r²

First, what is the equation of the circle?
(x–4)² + (y+1)² = (4√2)² = 16•2 = 32

then plug in the point to see if it fits
(x–4)² + (y+1)² = 32
(4–4)² + (–5+1)² = 32
0 + (–4)² = 32
16 = 32
not a match, so it is NOT on the circle.
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say: (x - 4)² + (y + 1)² = 32

P(4, - 5)

substitution...what do you get ? Come on...you can SUBSTITUTE !!

The point [P(4, - 5)] DOES NOT LIE ON THE CIRCLE DESCRIBED !
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kqftj say: jjgqauer
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