Given $$2b^2/a = 8$$ and $$3/\sqrt{5} = \sqrt{1 + b^2/a^2}$$ or $$4/5 = b^2/a^2$$ , find the required equation of the hyperbola.

The required equation of the hyperbola is $$x^2/25 - y^2/20 = 1$$ or $$4x^2 - 5y^2 = 100$$ .

The required equation of the hyperbola is $$x^2/20 - y^2/25 = 1$$ or $$5x^2 - 4y^2 = 100$$ .

The required equation of the hyperbola is $$x^2/16 - y^2/9 = 1$$ or $$9x^2 - 16y^2 = 100$$ .

The required equation of the hyperbola is $$x^2/9 - y^2/16 = 1$$ or $$16x^2 - 9y^2 = 100$$ .

If the foci are (0, ±4) = (0, ±be) ⇒ be = 4, and the vertices are (0, ±2) = (0, ±b) ⇒ b = 2 ⇒ a = 2√e, what is the equation of the hyperbola?

The equation is $$-x^2/(2\sqrt{5})^2 + y^2/(2)^2 = 1$$ or $$y^2/4 - x^2/20 = 1$$ .

The equation is $$x^2/4 - y^2/20 = 1$$ .

The equation is $$y^2/16 - x^2/4 = 1$$ .

The equation is $$x^2/20 - y^2/4 = 1$$ .

Given find the equation of the hyperbola.

The equation is $$x^2 - 11y^2 - 16xy - 12x + 6y + 21 = 0$$ .

The equation is $$x^2 + 11y^2 + 16xy + 12x - 6y - 21 = 0$$ .

The equation is $$x^2 - y^2 + 16xy - 12x + 6y + 21 = 0$$ .

The equation is $$x^2 - 11y^2 + 16xy - 12x + 6y - 21 = 0$$ .

If b = 4, $$2ae = 10$$ ⇒ $$16 = 25 - a^2$$ ⇒ $$a = 3$$ , what is the equation of the hyperbola?

The equation of the hyperbola is $$16x^2 - 9y^2 = 144$$ .

The equation of the hyperbola is $$9x^2 - 16y^2 = 144$$ .

The equation of the hyperbola is $$16x^2 + 9y^2 = 144$$ .

The equation of the hyperbola is $$9x^2 + 16y^2 = 144$$ .

If 2ae = 16, e = √2 ⇒ a = 4√2 and b = 4√2, what is the equation of the hyperbola?

The equation is $$x^2/(4\sqrt{2})^2$$ - $$y^2/(4\sqrt{2})^2$$ = 1 ⇒ $$x^2 - y^2 = 32$$ .

The equation is $$x^2/(4)^2 - y^2/(2\sqrt{2})^2 = 1$$ ⇒ $$x^2/16 - y^2/8 = 1$$ .

The equation is $$x^2/(8)^2$$ - $$y^2/(2)^2$$ = 1 ⇒ $$x^2/64$$ - $$y^2/4$$ = 1.

The equation is $$x^2/(2\sqrt{2})^2$$ - $$y^2/(4)^2$$ = 1 ⇒ $$x^2/8$$ - $$y^2/16$$ = 1.

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HYPERBOLA (EAMCET) EXERCISE

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MULTIPLE CHOICE QUESTION

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If the latus rectum of an hyperbola be 8 and eccentricity be 3/√5, then the equation of the hyperbola is

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MULTIPLE CHOICE QUESTION

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The equation of a hyperbola, whose foci are (5, 0) and (-5, 0) and the length of whose conjugate axis is 8, is

MULTIPLE CHOICE QUESTION

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The equation of the hyperbola referred to its axes as axes of coordinate and whose distance between the foci is 16 and eccentricity is √2, is

MULTIPLE CHOICE QUESTION

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The equation of the hyperbola referred to the axis as axes of co-ordinate and whose distance between the foci is 16 and eccentricity is √2, is

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