Question

Find an equation of the line tangent to the circle (x−2)2+(y−2)2=34
at the point (5,7).

Answer 1

do you know calculus? If so, take the derivative with respect to x and solve for dy/dx . This will give you an equation that gives the slope of the curve when you plug in an (x,y) point.

once you have the slope, you can use it and the point (4,11) to find the equation of the line tangent to the circle through point (4,11)

Answer 2

\[\frac{ d }{ dx }[(x-2)^{2} + (y-2)^{2}] = \frac{ d }{ dx } 34\]
\[2(x - 2) + 2(y - 2)\frac{ dy }{ dx } = 0\]
\[(y - 2)\frac{ dy }{ dx } = 2 - x\]
\[\frac{ dy }{ dx } = \frac{ 2 - x }{ y - 2 }\]
for point (5,7) plug into the equation:
\[\frac{ dy }{ dx } = \frac{ 2 -5 }{ 7 - 2 } = \frac{ -3 }{ 5 }\]

Answer 3

tangent line is perpendecular to the line that connects center of circle to the given point