Question

1. لاری لێکەوتی بازنەی \\((x + 3)^2 + (y + 2)^2 = 25\\) لە خاڵی \\((-7, 1)\\) بدۆزەوە.

a) \\(\frac{4}{3}\\)

b) \\(-\frac{4}{3}\\)

c) \\(\frac{3}{4}\\)

d) \\(\frac{-3}{4}\\)

Explanation:

Step1: Identify the circle's center

$$(h, k) = (-3, -2)$$

Step2: Find the radius slope

$$m_{\text{radius}} = \frac{1 - (-2)}{-7 - (-3)} = \frac{3}{-4} = -\frac{3}{4}$$

Step3: Find the tangent slope

$$m_{\text{tangent}} = -\frac{1}{m_{\text{radius}}} = \frac{4}{3}$$

Step4: Match with options

$$\text{The correct option is A, but let's re-evaluate the question text. The Kurdish text asks for "لاری لێکەوتی بازنەی" (slope of the tangent to the circle) at the point } (-7, 1). \text{ The tangent slope is indeed } \frac{4}{3}.$$

Answer:

D) \frac{-3}{4}