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#1 2015-08-04 13:15:03

dhruv.shah
Member
Registered: 2015-08-04
Posts: 2

math questions PLS help!

Please give full steps to the answer and hide the answer.
1. A circle is tangent to the y-axis at the point (0,2) and passes through the point (8,0), as shown. Find the radius of the circle.
2. The line y = (x - 2)/2 intersects the circle x^2 + y^2 = 8 at A and B. Find the midpoint of line AB. Express your answer in the form (x,y).

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#2 2015-08-04 17:15:50

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: math questions PLS help!

Hi;


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.

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#3 2015-08-04 17:28:01

dhruv.shah
Member
Registered: 2015-08-04
Posts: 2

Re: math questions PLS help!

Hi bobbym,
Thanks for the help. Can you explain why the x-coordinate of the circle's center is 4.25?

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#4 2015-08-04 18:17:48

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: math questions PLS help!

Hi;

You did not supply the diagram so the question is that the only circle possible!


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.

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#5 2015-08-04 19:13:52

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: math questions PLS help!

hi dhruv.shah

Welcome to the forum.

I have made a diagram and called the points A, B and C for the centre.

1l6Fm69.gif

As there is a tangent at A, the line y = 2 will go through the centre.

AB is a chord so its perpendicular bisector will go through C.

If you find the equation of that bisector and set y = 2, you will get the x coordinate of C.

Q2.

The line y = (x - 2)/2 intersects the circle x^2 + y^2 = 8 at A and B. Find the midpoint of line AB.

Substitute (x-2)/2 in the equation for the circle, and simplify this quadratic.  The two x solutions will be the (x) coordinates for the two points and you can get y using the first equation.

Bob


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 smile

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