AP EAMCET Engineering 22 Apr 2019 Shift 1 Paper

Simplify the given equation of parabola,
20(x2+y2−6x−2y+10) =(4x−2y−5)2
(x2+y2−6x−2y+10) =(

4x−2y−5

√20

)2
(x−3)2+(y−1)2 =(

4x−2y−5

√20

)2
The focus from above is (3,1) and equation of directrix is,
4x−2y−5=0
Thus, the distance from focus to directrix is,

|12−2−5|

√20

=

√5

2

=2a
So, the length of latus rectum is,
4a=2(2a)=2

√5

2

=√5