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Find the quadratic equation for the locus of points whose sum of its distance from (1, 0) and (−1, 0) is 6.

 

I know to start with sqrt( (x-1)^2 +y^2) + sqrt( (x+1)^2+y^2)=6, then square both sides. I'm not sure about the algebra after squaring both sides as I got that part wrong. 

 Mar 11, 2021
 #1
avatar+118069 
+2

We  have  an ellipse

 

The  focal points are (-1,0)  and (1,0)

 

Using symmetry, the center is (0, 0)

 

 

c  = the distance from the  center to either foci  =   1

 

The  sum of the distances from any point on the ellipse to the focal points = 2a

 

So

 

2a  = 6

a  =  3   ⇒   a^2  =  9

 

b^2  =  a^2  - c^2  =   9  - 1  =  8

 

The equation is

 

x^2/a^2   + y^2/b^2  = 1       .....so.....

 

x^2 / 9   +   y^2 / 8   =   1

 

 

cool cool cool

 Mar 11, 2021

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