Can I get admission in any B-school if I have a backlog in final year? Will I be allowed to take part in GD-PI?

Candidates can study Coordinate Geometry from How to Prepare for Quantitative Aptitude for CAT by Arun Sharma. Quantitative Aptitude for CAT by Nishit K. Sinha is another helpful resource. 

Yes. Coordinate Geometry is a useful topic in CAT Quant, especially for solving questions involving graphs, equations of lines, distances, slopes and geometric properties.

There is no fixed number of questions from Coordinate Geometry in CAT. Usually, one question may appear directly or indirectly through different topics.

Candidates can use How to Prepare for Quantitative Aptitude for CAT by Arun Sharma for concepts and graded practice. Quantitative Aptitude for CAT by Nishit K. Sinha is also a useful option. 

Yes. Linear Equations is an important topic for CAT Quant. Its concepts are used in questions based on ratios, mixtures, ages, time and work, profit and loss, etc.