+260 Prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x²+y²=5.
+118673 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.
