1 The coovdinate of the end point of a diancia of 1 circle zre \( \langle-5,3\rangle \) and \( \langle 3,-4\rangle \) Find 2. Equation of the curcle. 1) Lengtis of the diameter c Equation of the diameter

To find the coordinates of the midpoint (which is the center of the circle), you average the x-coordinates and the y-coordinates of the endpoints of the diameter: Midpoint = \(\langle \frac{-5 + 3}{2}, \frac{3 + (-4)}{2} \rangle = \langle -1, -\frac{1}{2} \rangle\). Next, the length of the diameter can be calculated using the distance formula: Length of diameter = \(\sqrt{(3 - (-5))^2 + (-4 - 3)^2} = \sqrt{64 + 49} = \sqrt{113} \approx 10.63\). Using the midpoint as the center \((h, k)\) and the diameter, the equation of the circle is \((x + 1)^2 + \left(y + \frac{1}{2}\right)^2 = \left(\frac{\sqrt{113}}{2}\right)^2\). The diameter's equation can be found using the points \((-5, 3)\) and \((3, -4)\). The slope \(m\) is \(\frac{-4 - 3}{3 - (-5)} = -\frac{7}{8}\), thus the equation of the diameter in point-slope form would be \(y - 3 = -\frac{7}{8}(x + 5)\). Now you've got the full circle picture, time to draw that bad boy!