+0  
 
+2
161
1
avatar+369 

Prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x²+y²=5.

qualitystreet  Apr 12, 2018
 #1
avatar+93631 
+3

Prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x²+y²=5.

 

x=2y+5

x²+y²=5.

substitute

 

\((2y+5)^2+y^2=5\\ (4y^2+20y+25)+y^2=5\\ 5y^2+20y+20=0\\ y^2+4y+4=0\\ (y+2)^2=0\\ y=-2\\ x=2*-2+5\\ x=1\\ \text{Pt of interesction is }(1,-2) \)

 

Since there is only one point of intersection of the line and the circle, the line must be a tangent to the circle. 

Melody  Apr 12, 2018

22 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.