What is the equation of the circle with center (-4,-3) that passes through the point (6,2)?
(x-4)2+(y-2)2=9
(x-3)2+(y+2)2=9
(x-3)2+(y+2)2=3
(x+3)2+(y-2)2=3
the distance between those two points is √125
The equation is
(x+4)^2 + (y+3)^2 = 125
You have mangled the question somehow. None of the equations has the correct center or radius.
Oh dear, it seems like you're trying to get into a "circle" of equations. But don't worry, I've got you covered! The correct equation for the circle with a center of (-4,-3) that passes through the point (6,2) is actually (x+3)² + (y+2)² = 3. Keep going, "center" yourself, and you'll solve it in no time!
To find the equation of the circle with center (-4, -3) that passes through the point (6, 2), you can use the general equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Plug in the given values:
(x + 4)^2 + (y + 3)^2 = r^2
Now, we need to find the value of r, which is the radius. The radius is the distance between the center of the circle and any point on the circle. In this case, we can use the given point (6, 2) to find the radius.
Using the distance formula:
r = √[(x2 - x1)^2 + (y2 - y1)^2]
r = √[(6 - (-4))^2 + (2 - (-3))^2]
r = √[(6 + 4)^2 + (2 + 3)^2]
r = √[(10)^2 + (5)^2]
r = √[100 + 25]
r = √125
Next, let's simplify the equation using the calculated radius:
(x + 4)^2 + (y + 3)^2 = 125
Expanding:
x^2 + 8x + 16 + y^2 + 6y + 9 = 125
Combine like terms:
x^2 + y^2 + 8x + 6y + 25 = 125
x^2 + y^2 + 8x + 6y - 100 = 0
Therefore, the equation of the circle with center (-4, -3) that passes through the point (6, 2) is:
x^2 + y^2 + 8x + 6y - 100 = 0.
To find the equation of a circle, we need the center coordinates and the radius. In this case, we have the center (-4,-3) and a point that lies on the circle (6,2).
The radius of the circle is the distance between the center and any point on the circle. We can use the distance formula to calculate the distance between the center and the given point:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Using the center (-4,-3) as (x1, y1) and the point (6,2) as (x2, y2), let's calculate the distance:
Distance = √[(6 - (-4))^2 + (2 - (-3))^2]
= √[10^2 + 5^2]
= √[100 + 25]
= √125
= 11.18 (rounded to two decimal places)
Now that we have the radius, we can write the equation of the circle in the standard form: (x - h)^2 + (y - k)^2 = r^2
Using the center (-4,-3) as the coordinates (h, k) and the radius value of 11.18 as r, we get:
(x - (-4))^2 + (y - (-3))^2 = 11.18^2
(x + 4)^2 + (y + 3)^2 = 125.01
Rounding the value of the radius, the equation of the circle is:
(x + 4)^2 + (y + 3)^2 = 125