Maths-

General

Easy

Question

# Tangents are drawn from the point (-1,2) on the parabola The length, these tangents will intercept on the line :

- 6
- 6
- 2
- none of these

Hint:

## The correct answer is: 6

### The length of tangent is asked to be find

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=0

Clearly, y1,y2 are the roots of the equation y2+2y−17=0

⇒y1+y2=−2

y1⋅y2=−17

Now, |y1−y2|=√(y1+y2)2−4y1⋅y2

=√22−4(−17)

=√72

=6√2

∴|y1−y2|=6√2

Hence finally the length is

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