The letters x and y represent rectangular coordinates Write

The letters x and y represent rectangular coordinates. Write the given equation using polar coordinates (r, theta). 5x^2 + 5y^2 = 2 Select the correct equation in polar coordinates below. r = 2/5(cos theta + sin theta) r^2 = 2/5 r^2 = 2/5(cos theta + sin theta) r = 2/5

Solution

5x²+5y²=2

5(x²+y²)=2

x=r cos theta, y=r sin theta

therefore

5(r² cos ² theta + r² sin ² theta=2

r²(5 cos² theta +5sin² theta)=2

r²=2/(5cos²theta +5sin²theta)

r²=2/(5(cos² theta +sin² theta))

r² =2/5

correct option is B.