csat-suneung 2014 Q8

csat-suneung · South-Korea · csat__math-B 3 marks Circles Tangent Lines and Tangent Lengths

In the coordinate plane, two lines $l _ { 1 } , l _ { 2 }$ tangent to the parabola $y ^ { 2 } = 8 x$ have slopes $m _ { 1 } , m _ { 2 }$ respectively. When $m _ { 1 } , m _ { 2 }$ are the two distinct roots of the equation $2 x ^ { 2 } - 3 x + 1 = 0$, what is the $x$-coordinate of the intersection point of $l _ { 1 }$ and $l _ { 2 }$? [3 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

In the coordinate plane, two lines $l _ { 1 } , l _ { 2 }$ tangent to the parabola $y ^ { 2 } = 8 x$ have slopes $m _ { 1 } , m _ { 2 }$ respectively. When $m _ { 1 } , m _ { 2 }$ are the two distinct roots of the equation $2 x ^ { 2 } - 3 x + 1 = 0$, what is the $x$-coordinate of the intersection point of $l _ { 1 }$ and $l _ { 2 }$? [3 points]\\
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5

Paper Questions

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