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  • A circle with radius 1 is tangent to the x-axis at the point (0,0). A line is tangent to the circle at the point (1,0). The line also passes through the point (2,3). Find the equation of

A circle with radius 1 is tangent to the x-axis at the point (0,0). A line is tangent to the circle at the point (1,0). The line also passes through the point (2,3). Find the equation of the line.

Option: 1

\mathrm{y=\frac{3}{2} x}
 


Option: 2

\mathrm{y=\frac{7}{2} x}
 


Option: 3

\mathrm{y^2=\frac{1}{2} x}

 


Option: 4

\mathrm{y=x^2 }


Answers (1)

best_answer

the center of the circle be \mathrm{(h, k)}
Since the circle is tangent to the \mathrm{\mathrm{x}-axis\, at \: (0,0), also \: \: k=0.}
Since the circle has radius 1 ,
Equation is \mathrm{(h-1)^2+k^2=1=h^2-2 h+1=0}
Factors are \mathrm{(h-1)^2=0}
So, \mathrm{\mathrm{h}=1,} the center of the circle is (1,0).
The line is tangent to the circle at (1,0) and the line's equation is of the form \mathrm{y=m x. }Putting in the point (2,3),
\mathrm{ \begin{aligned} & \Rightarrow 3=2 m \\ & \Rightarrow m=\frac{3}{2} \end{aligned} }

Therefore, the equation of the line is .\mathrm{y=\frac{3}{2} x}

The graph is 

Posted by

Ritika Kankaria

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