From a point `P(1,2)`
, two tangents are drawn to a hyperbola `H`
in which one tangent is drawn to each arm of the hyperbola. If the
equations of the asymptotes of hyperbola `H`
are `sqrt(3)x-y+5=0`
and `sqrt(3)x+y-1=0`
, then the eccentricity of `H`
is
2 (b) `2/(sqrt(3))`
(c) `sqrt(2)`
(d) `sqrt(3)`
Text Solution
AI Generated Solution
To solve the problem step-by-step, we will follow the reasoning presented in the video transcript and derive the eccentricity of the hyperbola based on the given information.
### Step 1: Identify the equations of the asymptotes
The equations of the asymptotes of the hyperbola \( H \) are given as:
1. \( \sqrt{3}x - y + 5 = 0 \) (let's call this \( L_1 \))
2. \( \sqrt{3}x + y - 1 = 0 \) (let's call this \( L_2 \))
### Step 2: Determine the slopes of the asymptotes
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From a point P(1,2) , two tangents are drawn to a hyperbola H in which one tangent is drawn to each arm of the hyperbola. If the equations of the asymptotes of hyperbola H are sqrt(3)x-y+5=0 and sqrt(3)x+y-1=0 , then the eccentricity of H is (a) 2 (b) 2/(sqrt(3)) (c) sqrt(2) (d) sqrt(3)
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