csat-suneung 2008 Q5

csat-suneung · South-Korea · csat__math-science 3 marks Conic sections Equation Determination from Geometric Conditions

The graph of the logarithmic function $y = \log _ { 2 } ( x + a ) + b$ passes through the focus of the parabola $y ^ { 2 } = x$, and the asymptote of the graph of this logarithmic function coincides with the directrix of the parabola $y ^ { 2 } = x$. What is the value of the sum $a + b$ of the two constants $a , b$? [3 points]
(1) $\frac { 5 } { 4 }$
(2) $\frac { 13 } { 8 }$
(3) $\frac { 9 } { 4 }$
(4) $\frac { 21 } { 8 }$
(5) $\frac { 11 } { 4 }$

The graph of the logarithmic function $y = \log _ { 2 } ( x + a ) + b$ passes through the focus of the parabola $y ^ { 2 } = x$, and the asymptote of the graph of this logarithmic function coincides with the directrix of the parabola $y ^ { 2 } = x$. What is the value of the sum $a + b$ of the two constants $a , b$? [3 points]\\
(1) $\frac { 5 } { 4 }$\\
(2) $\frac { 13 } { 8 }$\\
(3) $\frac { 9 } { 4 }$\\
(4) $\frac { 21 } { 8 }$\\
(5) $\frac { 11 } { 4 }$

Paper Questions

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