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RandomMathUsername

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Conic Questions

1) Square ABCD has side length 60. An ellipse E is circumscribed about the square and there is a point P on the ellipse such that PC = PD =50. What is the area of E?

2) Circle $\Gamma$ intersects the hyperbola y = 1/x at (1,1), (3,1/3), and two other points. What is the product of the y coordinates of the other two points?

I haz no idea or any thoughts on these two problems

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Conic Questions

Hi;

The fact that you know $ means you are experienced in the use of Latex on other forums, here we use the math tags for Latex. It also shows you know the rules that all other forums lay down. "No work, no answer"

I haz no idea or any thoughts on these two problems

None at all? The formula for the area of an ellipse and more is given here:

http://www.mathsisfun.com/geometry/ellipse.html

http://www.mathsisfun.com/area.html

Have any ideas now? Need more?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Conic Questions

hi RandomMathUsername

If you picked a name at random, how unlikely is your username?  Hhhmmm.   But welcome anyway!

I'm still thinking about Q1.

Here's my initial thoughts on Q2.

As those points are on the circle, the perpendicular bisector goes through the centre.  No other constraint so there are an infinite number of centres and circles.

My diagram shows two.  The products (only approximately here) seem to be the same, so I'm conjecturing the product is a constant whatever the circle.

So you could find the equation of the bisector, and obtain an expression for the radius and hence find the coordinates of the other two points.  Use the equation of the line to eliminate y (or x if you prefer) make the product, and hope that x (or y) cancels out of the result.

Good luck!

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Conic Questions

Hi Oran2009;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Conic Questions

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Conic Questions

Last edited by thickhead (2017-01-30 22:41:06)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}