Rectangular and polar coordinates Quiz 1

Question 1

When the location of the thief is traced on polar coordinates it is $$\left( 3,\dfrac{\pi }{2} \right)$$, then what is the location of the thief on the Cartesian plane?

Accepted Answer

$$\left( 0,	ext{ 3} ight)$$

Answer

$$\left( 2,	ext{ 0} ight)$$

Answer

$$\left( 3,	ext{ 0} ight)$$

Answer

$$\left( 0,	ext{ 2} ight)$$

Question 2

In a Cartesian plane, the position of a particle at any point $$\left( x,y ight)$$ can be determined by equation $${{y}^{2}}=axy-\dfrac{{{b}^{2}}{{x}^{3}}}{c{{y}^{3}}}$$. Then what is the polar equation for determining the position of a same particle at any point $$\left( r,	heta  ight)$$?

Accepted Answer

$${{r}^{2}}si{{n}^{2}}	heta =a{{r}^{2}}cos	heta sin	heta -\dfrac{{{b}^{2}}{{\cos }^{3}}	heta }{csi{{n}^{3}}	heta }$$

Answer

$${{r}^{2}}si{{n}^{2}}	heta =a{{r}^{2}}-\dfrac{{{b}^{2}}{{\cos }^{3}}	heta }{csi{{n}^{3}}	heta }$$

Answer

$${{r}^{4}}si{{n}^{4}}	heta =a{{r}^{6}}cos2	heta sin	heta -\dfrac{{{b}^{2}}{{\cos }^{6}}	heta }{c{{\cos }^{3}}	heta }$$

Answer

$$rsi{{n}^{2}}	heta =a{{r}^{3}}cos	heta sin	heta -\dfrac{{{b}^{2}}{{\cos }^{2}}	heta }{c{{\cos }^{3}}	heta }$$

Question 3

Two ships when placed on graph, Ship A is at point $$\left( 10\sqrt{5},{{	an }^{-1}}(2) ight)$$ when traced in polar coordinates and Ship B is at point $$\left( 20,30 ight)$$ when traced on rectangular coordinates. If it is given that $$\cos \left( {{	an }^{-1}}2 ight)=\dfrac{1}{\sqrt{5}}$$ and $$\sin \left( {{	an }^{-1}}2 ight)=\dfrac{2}{\sqrt{5}}$$, then what is the distance between Ship A and Ship B?

Accepted Answer

$$10\sqrt{2}	ext{ units}	ext{.}$$

Answer

$$20\sqrt{2}	ext{ units}	ext{.}$$

Answer

$$25\sqrt{2}	ext{ units}	ext{.}$$

Answer

$$50\sqrt{2}	ext{ units}	ext{.}$$

Question 4

Three boys were standing at points A $$\left( \sqrt{74},{{	an }^{-1}}\left( \dfrac{7}{5} ight) ight)$$, B $$\left( 6,8 ight)$$ and C $$\left( 7,9 ight)$$, where A point is traced on polar coordinates. If $$	ext{cos}\left( {{	an }^{-1}}\left( \dfrac{7}{5} ight) ight)	ext{=}\dfrac{5}{\sqrt{74}}$$ and $$sin\left( {{	an }^{-1}}\left( \dfrac{7}{5} ight) ight)=\dfrac{7}{\sqrt{74}}$$ then they were standing

Accepted Answer

in a straight line.

Answer

on the vertex of the triangle.

Answer

on the edge of the square.

Answer

on the points of the circle.

Question 5

On Cartesian plotting paper, it is seen that distance of house O from the house A at point $$\left( 1,2 \right)$$ and B at point $$\left( 7,2 \right)$$ which is twice to the distance from the house A, then at polar plotting paper, house O is at point

Accepted Answer

$$\left( \sqrt{13},	ext{ta}{{	ext{n}}^{-1}}\left( \dfrac{2}{3} ight) ight)$$

Answer

$$\left( 2,2 \right)$$

Answer

$$\left( 3,2 \right)$$

Answer

$$\left( 5,	ext{ta}{{	ext{n}}^{-1}}\left( \dfrac{2}{3} ight) ight)$$