+0

# 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.

0
41
3
+417

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.

michaelcai  Nov 6, 2017

#2
+5261
+1

The circle is tangent to the y-axis at  (0, 2) , so the y-coordinate of the center must be  2  .

We know..

(x - h)2 + (y - 2)2  =  r2      , where  h  is the x-coordinate of the vertex and  r  is the radius.

(0 - h)2 + (2 - 2)2  =  r2     →​     h2  =  r2     →     h  =  ± r

(8 - h)2 + (0 - 2)2  =  r2     →​     (8 - h)2 + 4  =  r2

In the last equation, substitute  ± r  in for  h .

(8 - ± r)2 + 4  =  r2

 (8 + r)2 + 4  =  r2 or (8 - r)2 + 4  =  r2 64 + 16r + r2 + 4  =  r2 64 - 16r + r2 + 4  =  r2 68 + 16r  =  0 68 - 16r  =  0 r  =  -68/16 r  =  68/16 r  =  -4.25 r  =  4.25

Since  r  is a distance,  r  =  4.25

Here is a graph: https://www.desmos.com/calculator/hipxsimqkb

hectictar  Nov 6, 2017
Sort:

#1
+78762
0

We need to see a diagram or -  at least -  know another point

CPhill  Nov 6, 2017
#2
+5261
+1

The circle is tangent to the y-axis at  (0, 2) , so the y-coordinate of the center must be  2  .

We know..

(x - h)2 + (y - 2)2  =  r2      , where  h  is the x-coordinate of the vertex and  r  is the radius.

(0 - h)2 + (2 - 2)2  =  r2     →​     h2  =  r2     →     h  =  ± r

(8 - h)2 + (0 - 2)2  =  r2     →​     (8 - h)2 + 4  =  r2

In the last equation, substitute  ± r  in for  h .

(8 - ± r)2 + 4  =  r2

 (8 + r)2 + 4  =  r2 or (8 - r)2 + 4  =  r2 64 + 16r + r2 + 4  =  r2 64 - 16r + r2 + 4  =  r2 68 + 16r  =  0 68 - 16r  =  0 r  =  -68/16 r  =  68/16 r  =  -4.25 r  =  4.25

Since  r  is a distance,  r  =  4.25

Here is a graph: https://www.desmos.com/calculator/hipxsimqkb

hectictar  Nov 6, 2017
#3
+78762
+1

Ah....thanks, hectictar.....I forgot about the word "tangent"    !!!!!

CPhill  Nov 7, 2017

### 4 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details