Eccentricity of conics Quiz 1

Question 1

If $$2a	ext{ and }2b$$ are the respective major and minor lengths of the ellipse such that $$9{{b}^{2}}={{a}^{2}}$$, then the eccentricity of an ellipse is equal to:

Accepted Answer

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

Answer

$$\dfrac{2}{5}$$

Answer

$$\dfrac{\sqrt{2}}{5}$$

Answer

$$\dfrac{4\sqrt{2}}{5}$$

Question 2

Find the length of the minor axis of an ellipse whose foci are $$\left( \pm 2\sqrt{15},0 \right)$$ and the eccentricity is given by $$\dfrac{\sqrt{15}}{11}$$.

Accepted Answer

$$4\sqrt{106}$$

Answer

$$3\sqrt{26}$$

Answer

$$3$$

Answer

$$2\sqrt{76}$$

Question 3

If the foci of the hyperbola are $$\left( 0,\pm 12 \right)$$, then find the equation of the hyperbola whose eccentricity is given by $$\dfrac{4}{5}$$.

Accepted Answer

$$9{{y}^{2}}-25{{x}^{2}}=2025$$

Answer

$$27{{y}^{2}}-5{{x}^{2}}=405$$

Answer

$$9{{x}^{2}}-125{{y}^{2}}=405$$

Answer

$$25{{x}^{2}}-16{{y}^{2}}=2025$$

Question 4

If $$\left( \pm a,0 ight)	ext{ and }\left( \pm c,0 ight)$$ are the vertices and foci of an ellipse respectively such that $$e=\dfrac{c}{12}	ext{ and }c=\dfrac{\sqrt{11}a}{6}$$, then find the equation of an ellipse?

Accepted Answer

$$\dfrac{{{x}^{2}}}{144}+\dfrac{{{y}^{2}}}{100}=1$$

Answer

$$\dfrac{{{x}^{2}}}{144}+\dfrac{{{y}^{2}}}{121}=1$$

Answer

$$\dfrac{{{x}^{2}}}{100}+\dfrac{{{y}^{2}}}{121}=1$$

Answer

$$\dfrac{{{x}^{2}}}{121}+\dfrac{{{y}^{2}}}{144}=1$$

Question 5

If the ellipse passing through the points $$\left( 2,1 ight)	ext{ and}\left( -1,-3 ight)$$ and whose foci are $$\left( 0,\pm c ight)$$, then the eccentricity of an ellipse is equal to:

Accepted Answer

$$\dfrac{\sqrt{10}}{4}$$

Answer

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

Answer

$$\dfrac{\sqrt{9}}{2}$$

Answer

$$\dfrac{11}{4}$$