**Core Concept**
Colposcopy is a diagnostic procedure that allows for a detailed examination of the cervix, vagina, and vulva for signs of disease. The presence of contact bleeding and a positive Pap smear indicates a high risk of cervical neoplasia, making colposcopy a critical next step in management.

**Why the Correct Answer is Right**
The correct answer is colposcopy because it enables a thorough examination of the cervix, allowing for the identification of abnormal cells or lesions that may not be visible to the naked eye. During colposcopy, a specialized instrument is used to magnify the area of concern, and a biopsy may be taken if abnormal cells are detected. This procedure helps to determine the extent of the disease and guide further treatment. Biopsy results will help in differentiating between low-grade and high-grade lesions, which is crucial for treatment planning.

**Why Each Wrong Option is Incorrect**
**Option A:** Conization of the cervix is not the next line of management in this scenario. Although conization may be necessary in some cases, it is typically reserved for situations where a definitive diagnosis cannot be made after colposcopy and biopsy.

**Option B:** Hysterectomy is a more invasive procedure that is usually reserved for cases where cervical cancer is diagnosed or in situations where conservative management is not feasible. It is not the next line of management for a patient with a positive Pap smear and contact bleeding.

**Option C:** Endocervical curettage (ECC) may be performed in conjunction with colposcopy to sample the endocervical canal, but it is not the primary next step in management for a patient with a positive Pap smear and contact bleeding.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that a positive Pap smear does not necessarily indicate cancer, but rather abnormal cell changes that may or may not progress to cancer. Colposcopy is a crucial diagnostic tool that helps differentiate between low-grade and high-grade lesions, guiding further treatment.

**Correct Answer:** C. Colposcopy.