Hyperbola Quiz 1

Question 1

Write the equation of hyperbola which has focal length as $$20$$ and transverse axis $$16$$.

Accepted Answer

$$ \dfrac{{{x^2}}}{{64}} - \dfrac{{{y^2}}}{{36}} = 1 $$

Answer

$$ \dfrac{{{x^2}}}{{64}} - \dfrac{{{y^2}}}{{49}} = 1 $$

Answer

$$ \dfrac{{{x^2}}}{{64}} + \dfrac{{{y^2}}}{{49}} = 1 $$

Answer

$$ \dfrac{{{x^2}}}{{64}} + \dfrac{{{y^2}}}{{36}} = 1 $$

Question 2

Write the equation of hyperbola which passes through the point $$\left( {8,14} \right)$$ and the transverse axis $$12$$.

Accepted Answer

$$  \dfrac{{{x^2}}}{{36}} - \dfrac{{{y^2}}}{{252}} = 1 $$

Answer

$$  \dfrac{{{x^2}}}{{36}} - \dfrac{{{y^2}}}{{25}} = 1 $$

Answer

$$  \dfrac{{{x^2}}}{{36}} + \dfrac{{{y^2}}}{{252}} = 1 $$

Answer

$$  \dfrac{{{x^2}}}{{36}} + \dfrac{{{y^2}}}{{25}} = 1 $$

Question 3

Find the point of intersection of hyperbola $${x^2} - 2{y^2} = 1$$ and the line $$x + y - 1 = 0$$

Accepted Answer

$$ \left( {1,0} \right) $$

Answer

$$ \left( { - 1,0} \right) $$

Answer

$$ \left( {0,1} \right) $$

Answer

$$ \left( {0, - 1} \right) $$

Question 4

The focal length of the rectangular hyperbola is $$\dfrac{8}{{\sqrt 2 }}$$. Find the equation of hyperbola.

Accepted Answer

$$  \dfrac{{{x^2}}}{{16}} - \dfrac{{{y^2}}}{{16}} = 1 $$

Answer

$$  \dfrac{{{x^2}}}{{16}} + \dfrac{{{y^2}}}{{16}} = 1 $$

Answer

$$  \dfrac{{{x^2}}}{{16}} - \dfrac{{{y^2}}}{{36}} = 1 $$

Answer

$$  \dfrac{{{x^2}}}{{16}} + \dfrac{{{y^2}}}{{36}} = 1 $$

Question 5

The equation of hyperbola is $$y = \dfrac{{x + 9}}{{x + 5}}$$. If tangent is passing through the origin then write its equation.

Accepted Answer

$$  x - 5y = 0 $$

Answer

$$  x + 5y = 0 $$

Answer

$$  25x + y = 0 $$

Answer

$$  25y + x = 0 $$