Problem Solving question with circles

[Aya]

1.what is the equation of the largest circle that can be incribed in a square of side length 9 units, if the diagonals of the square intersect at (-1,3).

where the radious is 9, but the ansewer in wrong
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2.Todd is flying his radio-controilled airplane abouve the ground in a circular path described by the equation (x-5)^2 + (y-2)^=36. Emiko is flying her plane at the same hightin a circullar path described by the euation
(x+1)^2 + (y-4)^2 = 25. do the pathes of the sirplaines intersect? If so,at how many points so they intersect?

how do I do this? Do i have to graph it?

 

[3trQN]

Make sure your calculating the formula for the right circle, An inscribed circle will have a diameter (twice the radius) equal to the width of your square, or a radius equal to half the squares width.

Thats r = (9/2)

Given that:
r^2 = (x-a)^2 + (y-b)^2 ---(1) for a point (x,y) on a circle centered at (a,b)

You know your center is at the center of the square, where the diagonals meet (-1,3).

Your calculation apears to be working out the radius of a circle that Circumscribes the square, not a Circle Inscribed by the square.

 

[Stephan Hoyer]

2.Todd is flying his radio-controilled airplane abouve the ground in a circular path described by the equation (x-5)^2 + (y-2)^=36. Emiko is flying her plane at the same hightin a circullar path described by the euation
(x+1)^2 + (y-4)^2 = 25. do the pathes of the sirplaines intersect? If so,at how many points so they intersect?

how do I do this? Do i have to graph it?

I think graphing it would give you the clearest and most obvious answer, although you could also solve it algebraically. Since these are equations of circles, graphing them should be very straightforward. I'm sure instructions on how to do this are in your text.

 

[arunbg]

First problem, go with 3trQN.

For the second problem, you can do it without graphing too.
First find the sum of the radii of the two circles.
Also find the distance between the centres of the circles.

What does comparing these distances suggest to you ?

 

[HallsofIvy]

2.Todd is flying his radio-controilled airplane abouve the ground in a circular path described by the equation (x-5)^2 + (y-2)^=36. Emiko is flying her plane at the same hightin a circullar path described by the euation
(x+1)^2 + (y-4)^2 = 25. do the pathes of the sirplaines intersect? If so,at how many points so they intersect?

You know
1) One circle is centered at (5,2) and the other at (-1,4).
2) The radii of the two circles are 6 and 5 respectively.

What is the distance between the two circles? Is it larger than or less than (or equal to) the sum of the two radii?