Question

A point ( x,y) moves so that the sum of the distance from the point (n,0) and (-n,0) is 2m .Prove that its equation of the locus x^2/m^2 +y^2/(m^2-n^2) = 1 .​

Answer 1

Answer:

Step-by-step explanation:

We know that,

Distance between point P and X-axis =y

Distance between point P and Y-axis =x

Distance between point P and given point (1,1)=

(x−1)

2

+(y−1)

2

​

Now,

According to given question

x+y=  

(x−1)

2

+(y−1)

2

​

x+y=  

x

2

+1

2

−2x+y

2

+1

2

−2y

​

On squaring both side and we get,

(x+y)

2

=  x

2

+y

2

−2x−2y+2

x

2

+y

2

+2xy=x

2

+y

2

−2x−2y+2

2xy=−2x−2y+2

xy=−x−y+1

xy+x+y−1=0

x(y+1)+y−1+(1−1)=0          on adding and subtracting  1 (one)

x(y+1)+y+1=2

x(y+1)+(y+1)=2

(y+1)(x+1)=2

This the locus of pointP(x,y).

=(x+1) (y+1)=2