A circle in the first quadrant with center on the curve y = 2x^2-27 is tangent to the y-axis and the line 4x = 3y. The radius of the circle is m/n where m and n are relatively prime positive integers. Find m + n.

Question

A circle in the first quadrant with center on the curve y = 2x^2-27 is tangent to the y-axis and the line 4x = 3y. The radius of the circle is m/n where m and n are relatively prime positive integers. Find m + n.

anonymous · Answer

|dw:1335052607712:dw| like this right?

anonymous · Answer

this is not my answer but that is the first quadrant

anonymous · Answer

right?

anonymous · Answer

are you sure? The question says that the circle is only in the first quadrant, not all 4 of them...

anonymous · Answer

@HyperChemist , nop, the cercle is only in the first quadrant

anonymous · Answer

anyone any idea? :S

mertsj · Answer

I'm thinking.  What class is this for?

anonymous · Answer

Well the center is where the equations y=2x^2-27 and 4x=3y. 
So basically (4/3)x=2x^2-27, and $$x=-7\sqrt{10}+2$$
$$7\sqrt{10}+2$$
Im a little stumped as to how to find the radius though

anonymous · Answer

Also the center would not be $$-7\sqrt{10}+2$$ because the domain of the functions are confined to the first quadrant

paxpolaris · Answer

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