Find the equation of the circle that passes through the point P(1, 7) and whose center is the point C(4, 3). Then sketch its graph.
you have the center at (4,3), so the equation is
(x-4)^2 + (y-3)^2 = r^2
Now you just need r. Since the point (1,7) is on the circle, plug it in:
(1-4)^2 + (7-3)^2 = 9+16 = 25
So,
(x-4)^2 + (y-3)^2 = 25
To find the equation of the circle that passes through point P(1, 7) with center C(4, 3), we can use the general equation of a circle.
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center is C(4, 3), so we have h = 4 and k = 3.
To find the radius r, we can use the distance formula between points P and C:
r = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates of P(1, 7) and C(4, 3), we have:
r = √((4 - 1)^2 + (3 - 7)^2)
= √(3^2 + (-4)^2)
= √(9 + 16)
= √25
= 5
So, the radius of the circle is 5.
Substituting the values of h, k, and r into the equation of the circle, we get:
(x - 4)^2 + (y - 3)^2 = 5^2
(x - 4)^2 + (y - 3)^2 = 25
This is the equation of the circle.
To sketch its graph, plot the center C(4, 3) and draw a circle with a radius of 5 units around it.