Tangents are drawn from the point (-1, 2) to the parabola $y^{2} = 4 x$ . The length of the intercept made by the line x = 2 on these tangents is

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6 \sqrt{2}

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2 \sqrt{6}

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none

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Solution

The correct option is B $6 \sqrt{2}$
If the line x = 2 intersects these tangents at (x,y1) and (x,y2) then the length of the intercept is given by |y1-y2|
$S S_{1} = T^{2} i s t h e e q u a t i o n o f p a i r o f t a n g e n t s \Rightarrow (y^{2} - 4 x) (8) = 4 (y - x + 1)^{2} \Rightarrow y^{2} - 2 y (1 - x) - (x^{2} + 6 x + 1) = 0 P u t x = 2 \Rightarrow y^{2} + 2 y - 17 = 0 \Rightarrow | y_{1} - y_{2} | = 6 \sqrt{2}$

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Tangents are drawn from the point (-1, 2) to the parabola y2=4x. The length of the intercept made by the line x = 2 on these tangents is

The correct option is B 6√2If the line x = 2 intersects these tangents at (x,y1) and (x,y2) then the length of the intercept is given by |y1-y2| SS1=T2istheequationofpairoftangents⇒(y2−4x)(8)=4(y−x+1)2⇒y2−2y(1−x)−(x2+6x+1)=0Put x=2⇒y2+2y−17=0⇒|y1−y2|=6√2

Tangents are drawn from the point (-1, 2) to the parabola $y^{2} = 4 x$ . The length of the intercept made by the line x = 2 on these tangents is