AP EAPCET 19-Aug-2021 Shift 1 Paper

Let L1:y=mx (equation of line passes through origin)
Intercept made by L1 and L2 are equal
⇒L1 and L2 are at the same distance from centre of circle x2+y2−x+3y=0
Now, centre (

1

2

,

−3

2

) ‌‌‌‌‌‌‌‌‌‌‌‌‌‌ [∵ centre = (-g - f)]
Distance of L1 from (

1

2

,−

3

2

)=

|m. 1 2 + 3 2 |

√m2+1

Distance of L2 from (

1

2

,−

3

2

)=

| 1 2 − 3 2 −1|

√1+1

∵L2:x+y−1=0 ‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌ [∵y=mx⇒mx−y=0]
⇒

| m+3 2 |

√m2+1

=

2

√2

Squaring both sides, we get

(m+3)2

4(m2+1)

=

4

2

⇒m2+6m+9=8(m2+1)
⇒7m2−6m−1=0
⇒m=

6±√36+28

14

=

6±8

14

=1,

−1

7

∴L1 is y=x
andy=

−1

7

x
or x−y=0
or x+7y=0