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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 $a$?

 Sep 11, 2023

Best Answer 

 #2
avatar+33616 
+1

I interpreted this question as follows:

 

 Sep 15, 2023
 #1
avatar+14964 
+1

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.

 

laugh  !

 Sep 14, 2023
edited by asinus  Sep 14, 2023
 #2
avatar+33616 
+1
Best Answer

I interpreted this question as follows:

 

Alan Sep 15, 2023

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