Locus

vice lord · 5 Nov 2009, 6:11 PM

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A circle passing though the origin O is tangent to the hyperbola xy = 1 at A , and intersects the hyperbola again at 2 distinct points B and C . Prove OA is perpendicular to BC

Aerath · 7 Nov 2009, 7:20 PM

I don't even understand how this question is possible....A circle with centre at origin, and a tangent to the hyperbola xy=1, would be tangent to both halves of the hyperbola, no?

gurmies · 7 Nov 2009, 7:59 PM

Quote:

Originally Posted by Aerath

I don't even understand how this question is possible....A circle with centre at origin, and a tangent to the hyperbola xy=1, would be tangent to both halves of the hyperbola, no?

It's not centered at the origin, it just passes through it. (x-a)^2 + (y-b)^2 = r^2, with the condition a^2 + b^2 = r^2.

Aerath · 8 Nov 2009, 10:07 AM

Oh. Yeah. Misread the question.

5 Nov 2009, 6:11 PM	#1 (permalink)
vice lord New Member HSC: 2009 Gender: Male Join Date: Sep 2009 Posts: 15 Last Activity: 10 Nov 2009, 7:09 PM	Locus You can hide this advertisement by registering. A circle passing though the origin O is tangent to the hyperbola xy = 1 at A , and intersects the hyperbola again at 2 distinct points B and C . Prove OA is perpendicular to BC

7 Nov 2009, 7:20 PM	#2 (permalink)
Aerath Prophet 9 <3 HSC: 2009 Gender: Male Location: Sydney Join Date: May 2007 Posts: 4,546 Last Activity: Today, 6:43 AM	Re: Locus I don't even understand how this question is possible....A circle with centre at origin, and a tangent to the hyperbola xy=1, would be tangent to both halves of the hyperbola, no? __________________

8 Nov 2009, 10:07 AM	#4 (permalink)
Aerath Prophet 9 <3 HSC: 2009 Gender: Male Location: Sydney Join Date: May 2007 Posts: 4,546 Last Activity: Today, 6:43 AM	Re: Locus Oh. Yeah. Misread the question. __________________

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