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A circle has equation (x + 2)^2 + (y + 3)^2 = 4 and a line has equation 5y − 4x + 10 = 0.

 (a) What is the distance from the center of the circle to the line?

 

(b) What is the greatest distance from a point on the circle to the line?

 Jan 9, 2021
 #1
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The center of the  circle is   (-2,-3)   and the radius  = 2

 

(a)  We  can use  the formula for the distance  from a point to a line to find this

 

D  = l -4(-2)+ 5(-3) + 10  ]             l  3 l

     ___________________  =   ________  units  ≈  .469 units

        sqrt  ( 4^2 + 5^2)                sqrt (41)

 

(b)  The greatest distance  from a point on the  cirlcle  to this line =  answer to (a)  +  radius  ≈

.469 + 2  =  2.469

 

 

cool cool cool

 Jan 9, 2021

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