Question

Find the equaiion of the bangen or circe at the given Point on the circle.

x²+3 x+y²-5 y=-5 ar (-1,3)

Answer 1

To find the equation of the tangent or circle at a given point on the circle, determine the center of the circle and calculate the slope of the line passing through the center and the given point. Since the slope is 1, the equation of the tangent is y - 3 = 1(x + 1).

Step-by-step explanation:

To find the equation of the tangent or circle at a given point on the circle, we need to first determine the center of the circle. We can rewrite the given equation of the circle as:

(x+1.5)² + (y-2.5)² = 33.25

This equation represents a circle with center at (-1.5, 2.5) and radius √33.25. To find the equation of the tangent at the point (-1, 3), we need to determine the slope of the line passing through the center and this point. The slope can be found using the formula:

slope = (3 - 2.5) / (-1 - (-1.5)) = 0.5 / 0.5 = 1

Since the slope is 1, the equation of the tangent is y - 3 = 1(x + 1).