(2x−3y−5)2=20(3x+2y+1) (Distance from Axis) ‌2= Latus-Rectum(Distance from tangent at vertex) ⇒(‌
2x−3y−5
√22+32
)‌ ‌‌=(‌
20
√32+22
)‌
(3x+2y+1)
√32+22
4× distance between tangent at vertex and directrix = Length of Latus-Rectum ∴ Distance between tangent at vertex and directrix =‌
5
√13
3x+2y+1=0:− Tangent at vertex 3x+2y+c=0:− Directrix ‌
|C−1|
√13
‌‌=‌
5
√13
C‌‌=1±5 ‌‌=6,−4 For C=−4 the line will be Latus-Rectum So, equation of directrix ⇒‌‌3x+2y+6=0 None of the given options are correct.