Step-by-step explanation:
y = (1 − 3x) / (x − 2)
Set the denominator to 0.
x − 2 = 0
x = 2
There is a vertical asymptote at x = 2.
Take the limit as x approaches ∞ and -∞.
lim(x→∞) y = -3
lim(x→-∞) y = -3
There is a horizontal asymptote at y = -3.
Plug in 0 for x and y.
y = (1 − 3(0)) / (0 − 2) = -1/2
0 = (1 − 3x) / (x − 2) → x = 1/3
There is a y-intercept at (0, -1/2) and an x-intercept at (1/3, 0).
The general form of the equation of a circle is,
x² + y² + Dx + Ey + F = 0, where D, E, F are constants.
The given equation is 7x² + 7y² − 28x + 42y − 35 = 0. So, to convert this equation into a general form we just need to get rid of the leading coefficient 7.
Hence, divide both sides of the equation by 7. So,
x² + y² − 4x + 6y − 5=0.
So, the general form of the equation is x² + y² − 4x + 6y − 5=0.