Answer:
Hyperbola
Step-by-step explanation:
The polar equation of a conic section with directrix ± d has the standard form:
r=ed/(1 ± ecosθ)
where e = the eccentricity.
The eccentricity determines the type of conic section:
e = 0 ⇒ circle
0 < e < 1 ⇒ ellipse
e = 1 ⇒ parabola
e > 1 ⇒ hyperbola
Step 1. <em>Convert the equation to standard form </em>
r = 4/(2 – 4 cosθ)
Divide numerator and denominator by 2
r = 2/(1 - 2cosθ)
Step 2. <em>Identify the conic </em>
e = 2, so the conic is a hyperbola.
The polar plot of the function (below) confirms that the conic is a hyperbola.
A. equation: y = -3x - 2
B. y-intercept: -2
<em><u>Solution:</u></em>
Given that,
<em><u>Write the equation 12x = - 4y - 8 in slope-intercept form</u></em>
The slope intercept form is given as:
Where,
m is the slope and "c" is the y intercept
From given
Thus the slope intercept form is found
Comparing with y = mx + c ,
c = -2
Thus the y intercept is -2