Given, equation is ‌2x2+5y−6x+1=0 ⇒2x2−6x+‌
9
2
+5y+1−‌
9
2
=0 ⇒2(x−‌
3
2
)2=−5(y−‌
7
10
) ⇒(x−‌
3
2
)2=‌
−5
2
(y−‌
7
10
)⇒X2=‌
−5
2
Y where X=x−‌
3
2
and Y=y−‌
7
10
Forvertex, on putting X=0,Y=0 ⇒‌‌x=3∕2‌ and ‌y=7∕10 ∴‌ Vertex ‌=(3∕2,7∕10) ‌ For focus, ‌X=0‌ and ‌Y=−a ⇒‌‌x=‌