a killer locus question (1 Viewer)

[darshil]

A is a point where the circle with equation x^2+y^2=16 cuts the X axis. Find the locus of the midpoints of all chords of this circle that contain the point A.

I tried to work backwards from the answer

x^2+y^2-4x

but i cant seem to click on it.

Any help is greatly appreciated. Thanks a truckload !

 

[Timothy.Siu]

i've already done this question on BOS before

let A be (4,0)
and P be some point on the circle (4sin @, 4cos @)

midpoint of AP (2+2sin @, 2cos @)

x=2+2sin @ and y=2cos @
x-2=2sin @

(x-2)^2=4sin^2@ y^2=4cos^2@

adding both equations,
(x-2)^2+y^2=4

 

[cookiesandcream]

does (-4,0) have to be considered? I think the pt (4,0) should be excluded from the solution, but i'm probably wrong

 

[Timothy.Siu]

does (-4,0) have to be considered? I think the pt (4,0) should be excluded from the solution, but i'm probably wrong

yeah ur right, and nah (-4,0) doesn't have to be considered,u just let A equal one of them,

 

[darshil]

Im sorry but I dont get it )=