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Question

# 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

A
6
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B
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C
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D
none
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Solution

## The correct option is B If the line x=2 intersects these tangents at (x1,y1) and (x2,y2) then the length of the intercept is given by |y1−y2| SS1=T2 is the equation of pair of tangents ⇒(y2−4x)(8)=4(y−x+1)2 ⇒y2−2y(1−x)−(x2+6x+1)=0 Put x=2⇒y2+2y−17=0Clearly, y1,y2 are the roots of the equation y2+2y−17=0⇒y1+y2=−2y1⋅y2=−17Now, |y1−y2|=√(y1+y2)2−4y1⋅y2=√22−4(−17)=√72=6√2∴|y1−y2|=6√2

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