Math Is Fun Forum

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

[ASK] Equation of a Circle

find standard eqations of circles that have centers on 4x+3y=8 and are tangent to both the line x+y=-2 and 7x-y=-6

What I got is

and

. Dunno how to continue from here.

Last edited by Monox D. I-Fly (2019-09-17 20:46:48)

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: [ASK] Equation of a Circle

hi Monox D. I-Fly

The angle bisector of the tangents will go through the centre of the circle.  This is generally true for circles and tangents … provable using congruent triangles,

So find where the  tangents cross.  A circle centred on this point with (0,6) on the circumference will also go through (-6,4) , which should help with getting the equation of the bisector.

Once you have the centre you can get the equation of a radial line from there to either tangent and hence the radius.

If you need more, I have a diagram.

LATER EDIT: Just re-read the question.  There are two solutions; the above method will find both, but I concentrated on the one with centre in the second quadrant.

Bob

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Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: [ASK] Equation of a Circle

Thank you.

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.