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

 Nov 9, 2019
 #1
avatar+106029 
+2

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

 

 

That will be your radius.

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
avatar+19773 
0

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.....   cheeky  

 Nov 9, 2019
 #3
avatar+106029 
+1

That is much more difficult  EP than simply using the perpendicular distance formula.

Melody  Nov 9, 2019
 #4
avatar+105411 
+2

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

 

 

cool cool cool

 Nov 9, 2019

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