There is exactly one value of $x$ for which the distance from $(5,6)$ to $(3x-1,ax+5)$ is $4$. If $a \neq 0,$ what is $a$?
+15000 What is a?
Hello Guest!
\((x-5^2)^2+(y-6)^2=4^2\\ y=3x-1\\ (x-5^2)^2+(3x-1-6)^2=4^2\\ x^2-10x+25+9x^2-42x+49-16=0\\ 10x^2-52x+58=0\\ x^2-5.2+5.8=0\\ x_{1,2}=2.6\pm\sqrt{2.6^2-5.8}\\ x\in \{1.620,\color{blue}3.580\}\)
\(y\in \{3.861,\color{blue}9.739\}\\ P_2\ (3.580,9.739)\\ P_1\ (0,5)\\ a= \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{9.739-5}{3.58-0}\\a=1.324\)
\(\color{blue}a\ is\ 1.324\)
With P3 (1.620,3.861) the further a can be calculated.
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