Polar and rectangular equations Quiz 1

Question 1

What is two times the rectangular equation of $$R=9$$.

Accepted Answer

$$2{{X}^{2}}+2{{Y}^{2}}=162$$

Answer

$$2{{X}^{2}}+2{{Y}^{2}}=98$$

Answer

$$2{{X}^{2}}+2{{Y}^{2}}=128$$

Answer

$$2{{X}^{2}}+2{{Y}^{2}}=242$$

Question 2

Find $$\sqrt{3}$$ the rectangular equation of  $$	heta =30{}^\circ $$.

Accepted Answer

$$3Y=X$$

Answer

$$Y=\sqrt{3}X$$

Answer

$$\sqrt{3}Y=X$$

Answer

$$Y=3X$$

Question 3

What is the rectangular equation of $$5R\sin 	heta =3\cot 	heta $$.

Accepted Answer

$$5{{Y}^{2}}=3X$$

Answer

$$5Y=3X$$

Answer

$$5Y=3{{X}^{2}}$$

Answer

$$5{{Y}^{2}}=3{{X}^{2}}$$

Question 4

What is the ratio of coefficient of $$\sin 	heta $$ in the polar equations of  $${{\left( X+3 ight)}^{2}}+{{\left( Y+6 ight)}^{2}}=45$$ and $${{\left( X+2 ight)}^{2}}+{{\left( Y+4 ight)}^{2}}=20$$.

Accepted Answer

$$\dfrac{3}{2}$$

Answer

$$\dfrac{1}{3}$$

Answer

$$\dfrac{1}{2}$$

Answer

$$\dfrac{2}{3}$$

Question 5

What is half of the polar equation of  $$4{{Y}^{2}}=3{{X}^{3}}$$

Accepted Answer

$$\dfrac{2}{3}{{	an }^{2}}	heta \sec 	heta $$

Answer

$$\dfrac{5}{3}{{\cot }^{2}}	heta \sec 	heta $$

Answer

$$\dfrac{2}{3}{{\sec }^{2}}	heta \cot 	heta $$

Answer

$$\dfrac{5}{3}	an 	heta \cos 	heta $$