fskilnik wrote:

[GMATH practice question]

Circle (x-3)^2 + (y-1)^2 = 13 intersects the vertical axis in two points which are p units apart. What is the value of p?

(A) 1/2

(B) 1

(C) 2

(D) 3

(E) 4

\(? = p\)

\(\left\{ \begin{gathered}

{\left( {x - 3} \right)^2} + {\left( {y - 1} \right)^2} = 13 \hfill \\

x = 0 \hfill \\

\end{gathered} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {y - 1} \right)^2} = 4\,\,\,\,\, \Rightarrow \,\,\,\left\{ \begin{gathered}

y - 1 = - 2 \hfill \\

\,\,\,\,\,{\text{OR}} \hfill \\

y - 1 = 2 \hfill \\

\end{gathered} \right.\)

\(\left\{ \begin{gathered}

x = 0\,\,\,;\,\,\,y - 1 = - 2\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{point}}\,\,\,A = \,\,\left( {0, - 1} \right) \hfill \\

\,\,\,\,\,{\text{OR}} \hfill \\

x = 0\,\,\,;\,\,\,y - 1 = 2\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{point}}\,\,B = \left( {0,3} \right) \hfill \\

\end{gathered} \right.\,\,\,\,\,\,\)

\(? = p = {\text{dist}}\left( {A,B} \right) = 4\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

_________________

Fabio Skilnik :: https://www.GMATH.net (Math for the GMAT)

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