Keratoconus (KC) is a corneal disorder that results in blurry and distorted vision. Traditional diagnostic tools, while effective, are often bulky, costly, and require professional operation. In this paper, we present a portable and innovative methodology for diagnosing. Our proposed approach first captures the image reflected on the eye's cornea when a smartphone screen-generated Placido disc sheds its light on an eye, then utilizes a two-stage diagnosis for identifying the KC cornea and pinpointing the location of the KC on the cornea. The first stage estimates the height and width of the Placido disc extracted from the captured image to identify whether it has KC. In this KC identification, k-means clustering is implemented to discern statistical characteristics, such as height and width values of extracted Placido discs, from non-KC (control) and KC-affected groups. The second stage involves the creation of a distance matrix, providing a precise localization of KC on the cornea, which is critical for efficient treatment planning. The analysis of these distance matrices, paired with a logistic regression model and robust statistical analysis, reveals a clear distinction between control and KC groups. The logistic regression model, which classifies small areas on the cornea as either control or KC-affected based on the corresponding inter-disc distances in the distance matrix, reported a classification accuracy of 96.94%, which indicates that we can effectively pinpoint the protrusion caused by KC. This comprehensive, smartphone-based method is expected to detect KC and streamline timely treatment.