Tessellate S.T.E.M.S (2019) - Mathematics - Category B - Set 1 - Objective Problem 5

Geometry Level 3

Find the largest value of y x \dfrac{y}{x} , where ( x , y ) (x,y) is real number pair satisfying ( x − 3 ) 2 + ( y − 3 ) 2 = 6 (x-3)^2 + (y-3)^2=6 .

This problem is a part of Tessellate S.T.E.M.S. (2019)

6 + 2 3 6+2\sqrt{3} 2 + 3 2+\sqrt{3} 3 + 2 2 3+2\sqrt{2} 2 3 2\sqrt{3}

Tessellate S.T.E.M.S. Mathematics by Tessellate S.T.E.M.S. Ma… , 26

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1 solution

Parth Sankhe
Oct 15, 2018

The given equation is of a circle, centred at ( 3 , 3 ) (3,3) and having radius = √6. The highest value of y x \frac {y}{x} means the highest value of slope of a line through origin which intersects or touches the circle.This highest slope would be of the tangent to the circle from origin (having slope > 1 >1 ). The slope of this tangent comes out to be 3 + √8

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