X^2 + y^2 - 6x + 8y = 144
1 answer:
The diameter of the equation of a circle in the xy-plane as shown is 26 units.
The standard form for finding the equation of a circle is expressed as:
For us to get the diameter of the circle, we need to get the radius of the circle first calculated as shown:
Given the equation of the circle expressed as
Compare with the general formula:
2gx = -6x
g = -6/2
g = -3
Similarly;
2fy = 8y
2f = 8
f = 4
C = -144
Substitute into the formula for calculating the radius;
Get the diameter of the circle
d = 2r
d = 2(13)
d = 26 units
Hence the diameter of the equation of a circle in the xy-plane as shown is 26 units.
Learn more here: brainly.com/question/12908710
You might be interested in
Answer:
29% of the drive
Step-by-step explanation:
The plot of the problem is:
Transmitter at origin (0,0)
City to the north at (0,70)
City to the east at (74,0)
The path from city to city is a line with slope:
m = (-70)/74 = -35/37
and y-intercept at y = 70, so the equation is y = (-35/37)*x + 70.
The transmitter reach the area enclosed by the next circle:
x^2 + y^2 = 53^2
See the picture attached
The intersection is gotten from the picture or solving:
x^2 + [(-35/37)*x + 70]^2 = 53^2
the points approximately are: (24.1, 47.2) and (45.8, 26.7)
From Pythagorean theorem the total distance of the trip is:
d1 = √(70^2 + 74^2) ≈ 101.9 miles
And the distance when the signal is picked up is:
d2 =√ [(45.8 - 24.1)^2 + (47.2 - 26.7)^2] ≈ 29.9 miles
You will pick up a signal from the transmitter in (d2/d1)*100 = 29% of the drive.
