Circle C is centered at (-4,3). Write the equation of the line tangent to circle C at point P(2,5). (point-slope form)
To find the equation of the line tangent to the circle at a given point, we need to find the slope of the tangent line and then use the point-slope form.
Step 1: Find the slope of the line passing through the center of the circle and the given point. We can do this using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's substitute the given values:
(x1, y1) = (-4, 3)
(x2, y2) = (2, 5)
slope = (5 - 3) / (2 - (-4))
slope = 2 / 6
slope = 1/3
Step 2: Now we have the slope, we can use the point-slope form of a line to find the equation of the tangent line. The point-slope form is given by:
y - y1 = m(x - x1)
Substitute the given values into the equation:
(x1, y1) = (2, 5)
m = 1/3
y - 5 = (1/3)(x - 2)
This is the equation of the tangent line to the circle C at point P(2,5) in point-slope form.