csat-suneung 2013 Q7

csat-suneung · South-Korea · csat__math-science 3 marks Conic sections Tangent and Normal Line Problems
The tangent line at the point $( b , 1 )$ on the hyperbola $x ^ { 2 } - 4 y ^ { 2 } = a$ is perpendicular to one asymptote of the hyperbola. What is the value of $a + b$? (Given that $a , b$ are positive numbers.) [3 points]
(1) 68
(2) 77
(3) 86
(4) 95
(5) 104 
The tangent line at the point $( b , 1 )$ on the hyperbola $x ^ { 2 } - 4 y ^ { 2 } = a$ is perpendicular to one asymptote of the hyperbola. What is the value of $a + b$? (Given that $a , b$ are positive numbers.) [3 points]\\
(1) 68\\
(2) 77\\
(3) 86\\
(4) 95\\
(5) 104
Paper Questions
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