An algebra problem by Tiger Ang

Algebra Level 3

Without graphing the equation, what is the graph of ( x + 2 ) 2 + y 2 + x 2 + ( y − 2 ) 2 = 6 \sqrt { { (x+2) }^{ 2 }+{ y }^{ 2 } } +\sqrt { { x }^{ 2 }+{ (y-2) }^{ 2 } } =6 ?

Straight Line Ellipse Parabola Hyperbola Circle

Tiger Ang by Tiger Ang , 20, Malaysia

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1 solution

Arjen Vreugdenhil
Jan 13, 2018

The solution set consists precisely of those point P ( x , y ) P\:(x,y) for which the sum of the distance to point A ( − 2 , 0 ) A\:(-2,0) and the distance to point B ( 0 , 2 ) B\:(0,2) is equal to 6: that is, d ( A , P ) + d ( B , P ) = 6 d(A,P) + d(B,P) = 6 .

It is well-known that such a set of points is an ellipse \boxed{\text{ellipse}} .

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