TS EAMCET 7 May 2018 Shift 1 Solved Paper

Section: Mathematics

Question : 54 of 160

Marks: +1, -0

If two distinct chords drawn from the point A(4 , 4) oil the parabola y2 = 4x are bisected by the line y = ax. then the interval in which a lies is

(
1
2
−
1
√2
,
1
2
+
1
√2
)
(−
√3
2
,
1
2
)
(
1+√2
2
,
5+√2
2
)
(2 , ∞)

Validate

Solution:

Let the point of intersection of the line y=mx with the chord be (n,an)
Then n=

4+x1

⇒x1=2n−4

an=

4+y1

⇒y1=2an−4
since (x1,y1) is on the parabola then,
(2an−4)2=4(2n−4)
4a2n2+16−16an=8n−16
4a2n2−16an−8n+32=0
4a2n2−(16a+8)n+32=0
To have two distinct chords, D>0.
(16a+8)2−4(4a2)(32)>0
64(2a+1)2−512a2>0
(2a+1)2−8a2>0
4a2−4a+1<2
(2a−1)2<2
−√2<(2a−1)<√2
$ {1-\√ {2}}/{2}

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