Some Circle Locus Questions (1 Viewer)

[nrlwinner]

I've nearly finished this exercise, but the final 3 questions I just plain do not get.

12)

A point P(x,y) moves so that its distance from (3,4) is proportional to its distance from (-1,2). Find the equation of the locus of P if the origin is a point on the locus.

13)

A is a point where the circle with the 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.

14)

Find the equation of the locus of the midpoins of all chords of length 4 units of the circle with equation x^2 + y^2 -4x +2y = 4

 

[gurmies]

12)



I think the rest is straightforward....

 

[nrlwinner]

Thanks, explained perfectly. Can anyone help me with the other 2?

 

[addikaye03]

14)

Find the equation of the locus of the midpoins of all chords of length 4 units of the circle with equation x^2 + y^2 -4x +2y = 4

x^2-4x+y^2+2y=4

(x^2-4x+4)+(y^2+2y+1)=4+4+1

(x-2)^2+(y+1)^2=9 [Since (x-a)^2+(y-b)^2=r^2]

Centre (2,-1) Radius=3

Can you see where to go next?

 

[study-freak]

 

[nrlwinner]

x^2-4x+y^2+2y=4

(x^2-4x+4)+(y^2+2y+1)=4+4+1

(x-2)^2+(y+1)^2=9 [Since (x-a)^2+(y-b)^2=r^2]

Centre (2,-1) Radius=3

Can you see where to go next?

I can get up to this point. It's just I don' know what to do next.

 

[lolokay]

I can get up to this point. It's just I don' know what to do next.

have you drawn a diagram of the situation?

 

[nrlwinner]

have you drawn a diagram of the situation?

Is it centre (2,-1) radius root 5?

 

[addikaye03]

Is it centre (2,-1) radius root 5?

radius 3 centre (2,-1), see my above working

 

[lolokay]

Is it centre (2,-1) radius root 5?

yeah