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# help

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write the equation of center 3,4 tangent to 2x+y+5=6

Nov 9, 2019

#1
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You need to use the perpendicular distance formula to find the distance between the line and the point (3,4)

Then it is the same as the last question.

Have a go.

Here is the formula with an example of how to use it. Nov 9, 2019
#2
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Put the equation into   y = mx + b form:

y = -2x +1      now you hve slope, m      m = -2   the perpindicular slope will be  - 1/m = -1/-2 = 1/2

Now you have a point (3,4 ) and the slope....   can you find the equation of the line with slope = 1/2   and point 3,4  ?

draw that line..... then you can find the radius of your circle quite easily.....

Remember the equation of a circle?   (x-h)^2 + (y-k)^2 = r^2  ????       (h,k) is the center of the circle......

Let us know what you find for an answer..... Nov 9, 2019
#3
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That is much more difficult  EP than simply using the perpendicular distance formula.

Melody  Nov 9, 2019
#4
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We can use the "formula" for the distance from a point to a line to solve this

The line  is     2x + y -1   = 0

So we have that

l  2(3) + 4 - 1 l            l  9  l             9

____________  =     ____   =      ___     this is the radius of the circle

√[2^2 + 1^2 ]             √5               √5

The equation of the circle is

(x - 3)^2  +  ( y - 4)^2  =   81/5

Here  is a graph  : https://www.desmos.com/calculator/b8fxaseqdv   Nov 9, 2019