Question

Eliminate the parametric terms x=6cos(θ) and y=7sin(θ). The resulting equation is

A) x² + y² = 1
B) x² - y² = 1
C) x² + 7y² = 36
D) x² - 6y² = 1

Answer 1

To eliminate the parametric terms, exploit the Pythagorean identity to get x2 + 7y2 = 36, which matches option C).

Step-by-step explanation:

To eliminate the parametric terms x=6cos(θ) and y=7sin(θ), we need to exploit the Pythagorean identity sin2(θ) + cos2(θ) = 1. By dividing the equation x by 6 and y by 7, and then squaring both sides, we get:

• (x/6)2 = cos2(θ)
• (y/7)2 = sin2(θ)

Adding the resulting equations gives us:

(x/6)2 + (y/7)2 = cos2(θ) + sin2(θ)

Since cos2(θ) + sin2(θ) = 1, then:

(x/6)2 + (y/7)2 = 1

Multiplying through by 36 yields:

x2 + 7y2 = 36, which is option C).