+0  
 
0
91
1
avatar

A circle has the equaton (x-2)^2+(y+3)^2=4 and a line has the equation 5y-4x+20=0. 

 

a) What is the distance from the center of the circel to the line. 

 

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

 

Thanks!

 Jun 15, 2020
 #1
avatar+8341 
0

a)
Center = (2, -3).

 

Using the point-line distance formula: 

\(\quad \text{Distance between }(x_0, y_0)\text{ and the line }ax+by+c=0\\ = \dfrac{\left|ax_0 + by_0 + c\right|}{\sqrt{a^2 + b^2}}\)

 

Plugging in \((x_0, y_0, a, b, c) = (2, -3, -4, 5, 20)\) gives the answer.

 

b)

In this case, you plot a straight line perpendicular to 5y - 4x + 20 = 0, which passes through the center of the circle. This straight line intersects the circle twice. For each intersection, calculate the point-line distance between the intersection and the straight line 5y - 4x + 20 = 0. The smaller one is the minimum distance, and the larger one is the required answer.

 Jun 15, 2020

16 Online Users

avatar