Answer:
Explanation:
We can use the identity:
cos(θ) = x/r
sin(θ) = y/rSubstituting these into the given equation, we get:r(1-5 cos(θ)) = 7
r - 5r cos(θ) = 7
sqrt(x^2+y^2) - 5(x^2+y^2)/(sqrt(x^2+y^2)) = 7
Let's multiply both sides by sqrt(x^2+y^2) to eliminate the denominator:x^2 + y^2 - 5x^2 cos(θ) - 5y^2 sin(θ) = 7 sqrt(x^2+y^2)Substituting cos(θ) = x/r and sin(θ) = y/r, we get:x^2 + y^2 - 5x^2(x/sqrt(x^2+y^2)) - 5y^2(y/sqrt(x^2+y^2)) = 7 sqrt(x^2+y^2)Simplifying the expression, we get:6x^2 + 6y^2 = 7sqrt(x^2 + y^2)Squaring both sides of the equation, we get:36x^4 - 84x^2y^2 + 36y^4 - 49x^2 - 49y^2 = 0Therefore, the rectangular equation of the conic section is:36x^4 - 84x^2y^2 + 36y^4 - 49x^2 - 49y^2 = 0.