Circles and ellipses Quiz 1

Question 1

Veronica wants to find what the equation  $${{x}^{2}}+{{y}^{2}}-6y=0$$  represents from the conic sections. Help her in finding this.

Accepted Answer

Circle

Answer

Pair of straight lines

Answer

Ellipse

Answer

Parabola

Question 2

Anulatha wishes to map the curve with eccentricity as  $$\dfrac{4}{5}$$. She notices that the foci of this curve lies on $$(0,\pm 4)$$. Find the equation to map it.

Accepted Answer

$$\dfrac{{{x}^{2}}}{9}+\dfrac{{{y}^{2}}}{25}=1$$

Answer

$$\dfrac{{{x}^{2}}}{25}+\dfrac{{{y}^{2}}}{9}=1$$

Answer

$$\dfrac{{{x}^{2}}}{9}\pm \dfrac{{{y}^{2}}}{25}=1$$

Answer

$$\dfrac{{{x}^{2}}}{25}\pm \dfrac{{{y}^{2}}}{9}=1$$

Question 3

A printer is set to make a circular image given by the equation $${{x}^{2}}-6x+{{y}^{2}}-4y-12=0$$ . If it needs to be printed on a square sheet such that minimum wastage of sheet occurs, find the length of the square sheet.

Accepted Answer

10 units

Answer

14 units

Answer

11 units

Answer

12 units

Question 4

An astronomer tries to map the latus rectum of an elliptical trajectory of a star on his software such that the foci is $$(0,\pm 4)$$, the directrix is found to be along $$y=\pm 9$$. Help her in doing so.

Accepted Answer

$$\dfrac{20}{3}$$

Answer

$$\dfrac{20}{7}$$

Answer

$$\dfrac{10}{3}$$

Answer

$$\dfrac{10}{7}$$

Question 5

Two gears of uniform circular shape are to be used in a machine, they are given by equations $${{x}^{2}}+{{y}^{2}}+2x+4y-3=0	ext{ and }{{	ext{x}}^{2}}+{{y}^{2}}+2x-8x-6y+7=0$$. What would be the optimum distance between the gears so that they touch?

Accepted Answer

$$7.07units$$

Answer

$$0unit{{s}^{{}}}$$

Answer

$$6unit{{s}^{{}}}$$

Answer

$$\dfrac{16}{9}units$$