Answer:
Equation 1: r = -5 * cos theta
Equation 2: r = 1 – ( 4 * sin theta )
Step-by-step explanation:
Graph 1:
This graph is a circle along negative x- axis.
General equation for graph:
R = a cos theta ∴ a = diameter of circle
From given graph, it is included that:
a = -5
a/2 = -2.5 (center of circle)
Equation 1: r = -5 cos theta
Graph 2:
This graph is an inner-loop limacon.
The inner-loop limacon is in the downward direction along the negative y-axis
The general equation for the graph will be :
r = a – b sin theta
a will represent x – intercept, from graph it is included that:
a = { +1, -1 }
For inner-loop on y-axis, b - a = 3 ………….1
For outer-loop on y-axis, a + b = 5 …………2
Adding both 1 and 2 to find values of a and b
b – a = 3
a + b = 5
2b = 8 ⇒ b = 4
Putting value of b in 2
a + 4 = 5 ⇒ a = 1
substituting values of a and b in general equation:
Equation 2: r = 1 – 4 sin theta
