Question

a circle is centered at the point (5,-4) and it passes through the point (-3,2). the equation of this circle is (x+ )^2+(y+ )^2=

Answer 1

Remember that the general formula for a circle is  (x – h)² + (y – k)² = r², where (h,k) is the coordinate of the center. We already know that (h,k) = (5,-4), since we know the center's coordinates. We need to find r, the radius, using the distance between the center and the point (-3,2). To do this, we can either use the distance formula, or plug in the points in our circle equation and solve for r.Let's do the second one, plugging in and solving for r.We can use the point (-3,2) for (x,y):(x – h)² + (y – k)² = r²(-3 - 5)² + (2 - -4)² = r²(-8)² +(6)² = r²64 + 36 = r²100 = r²r = 10We know that r=10, and that r² = 100Using h, k, and r, we can now solve for the equation of the circle in standard form.The equation of the circle is:(x – 5)² + (y + 4)² = 100

Answer 2

The final equation is (x-5)^2 + (y+4)^2 = 10^2. 

Hopefully this'll help you!