Do it for your name
If 5 x 2 + 5 y 2 − 3 4 x + 7 0 y + 5 8 = 0 , what is the value of
( x + 2 ) 2 + ( y − 2 ) 2 ( 1 − x ) 2 + ( y + 3 ) 2 equal to?
Your answer will be of the form b a where a and b are positive coprime integers. Enter your answer as a + b .
The answer is 13.
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1 solution
Pretty much the same type of playing around with the algebra as you, so no point in me posting another solution.
Also, I believe you meant ( y − 2 ) 2 instead of just ( y − 2 ) ? Could you please edit it as to not confuse others? Thanks.
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Thanks ! I have made the necessary changes .
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You're welcome!
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@Tai Ching Kan – Does this problem ring a bell ? Something related to geometry ............
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@Raven Herd – To be honest, I've never seen a question asked like this before, but I've done questions where you had to solve two conics simultaneously.
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@Tai Ching Kan – Alright ! I won't keep secrets any longer . There is a point A(1,-3) and a point B(-2 , -2) and another point P (x,y) in the coordinate plane . Now , the very first equation which I gave is the condition for which P divides the line segment AB in the ratio of 2 : 3 .If you bear that context in mind , this question is a piece of cake : D