عَلَى الْهُدَى

عَلَى الْهُدَى is a phrase (شِبْهُ الجُمْلَةِ) consisting of a particle of pulling down (preposition) and a genitive noun

PhraseParticle / NounNoun Particle
شِبْهُ الجُمْلَةِجَارٌ وَمَجْرُوْرٌاسْمٌ مَجْرُوْرٌحَرْفُ جَرٍّ
PhraseCompoundGenitive NounParticle of pulling down
  
on the guidanceعَلَى الْهُدَى=الهُدَى+عَلَى 
on the guidancethe guidanceon
Surah/Below are the 3 verses in the holy Quran containing the genitive compoundعَلَى الْهُدَى
Verse
and if their aversion (turning away) be great upon youوَإِنْ كَانَ كَبُرَ عَلَيْكَ إِعْرَاضُهُمْ
then if you are able to seek a way down into the earthفَإِنِ اسْتَطَعْتَ أَنْ تَبْتَغِيَ نَفَاقًا فِي الأَرْضِ
or a way up to the heaven so that you may bring them a signأَوْ سُلَّمًا فِي السَّمَآءِ فَتَأْتِيَهُمْ بِئَايَةٍ
and had Allah (SWT) willed, surely, He could have gathered them to the guidanceوَلَوْ شَآءَ اللهُ لَجَمَعَهُمْ عَلَى الهُدَى
6-35so, you do not ever remotely be of the ignorantفَلَا تَكُونَنَّ مِنَ الجَاهِلِيْنَ
41-17 
104-7Do you consider that he is on the guidanceأَرَءَيْتَ إِنْ كَانَ عَلَى الْهُدَى