Home > Graphing > Lines intersecting circles

Lines intersecting circles

When a line intersects a circle it will either have one point of contact in which case it is a tangent to the circle or it will cut it in two places.

To find the points of contact between a line and a circle

  1. If needed, rearange the equation of the line to make x or y the subject
  2. Substitute into the circle equation and solve the resulting quadratic
  3. Substitute the solutions into the equation of the line to get the required coordinates

Example

Find where the line y=2x+1 intersects with the circle (x+2)^2+(y-1)^2=5

When we substitute y into the circle we get (x+2)^2 + ((2x+1)-1)^2=5

\therefore (x+2)^2+(2x)^2=5 \Rightarrow x^2+4x+4+4x^2=5 \Rightarrow 5x^2+4x-1=0

\therefore (5x-1)(x+1)=0 \Rightarrow x=\frac{1}{5} or x = -1

If x=\frac{1}{5}, y=\frac{7}{5}

If x=-1, y=-1

\therefore the points of intersection are (\frac{1}{5}, \frac{7}{5}) and (-1,-1)

Advertisements
Categories: Graphing
  1. No comments yet.
  1. No trackbacks yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: