circles,tangents problem...

hello guys a new member here..

i need help with this math problem that i got recently... its in the chapter conic sections.

the question is:

Find the equation of the tangent to the circle

if the equation of the circle is give by x^2+y^2-4x+6y-12=0 and is parallel to the line having the equation given by x+y-8=0

any help would be appreciated :)..

cheers.

EDIT: last question was wrong and i updated it with a valid question.

thx for the response.

Re: circles,tangents problem...

Quote:

Originally Posted by

**GalXiOn** Find the equation of the tangent to the circle

Given: eq. of circle - x^2-4x-6y-12=0 and tangent is parallel to the line given by the equation 4x-3y=1.

There is something wrong with the question.

**is not a circle**.

Please check the wording of that question.

Re: circles,tangents problem...

Quote:

Originally Posted by

**Plato** There is something wrong with the question.

**is not a circle**.

Please check the wording of that question.

umm in my book it says if the equation if of the form x^2+y^2+2gx+2fy+c=0 then it is a General form i.e it represents the circle.

Re: circles,tangents problem...

Quote:

Originally Posted by

**GalXiOn** umm in my book it says if the equation if of the form x^2+y^2+2gx+2fy+c=0 then it is a General form i.e it represents the circle.

But what you posted is not a circle there is no

Re: circles,tangents problem...

Quote:

Originally Posted by

**Plato** But what you posted is not a circle there is no

EDIT: updated.... (question given was wrong Sorry.. updated now...)

Re: circles,tangents problem...

well if not that,what about this one? :

x^2+y^2-4x+6y-12=0 and parallel to line having the equation x+y-8=0.. will this work?.. im just listing out a few sums that i got recently.. ive never seen these sorta sums before.. and are totally new.. im guessing its gotta do something with comparing the radius using 2 different formulas to get a variable.. something like equating (|ax1+by1+c|)/ sqrt(A^2+b^2) which is the distance from a line and a point

and this formula: sqrt(g^2+f^2-c) which is the radius of the circle if g,f,c is known to us(which can be found using the given equation) g is -2 and f is -3..(im not sure..)

now i dont know how to proceed or i dont know if it is even the right way to approach.. ..

Re: circles,tangents problem...

Re: circles,tangents problem...

Quote:

Originally Posted by

**Plato** By completing squares that circle is

.

The slope of any non-vertical tangent is

where

and

.

The slope of the line

is

So find points

where slope is

.

hmm thx i'll try it out..