Hyperbola

### Find the (v) length of the rectum of each of the following the hyperbola :

Given Equation: $\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{4}=1$ Comparing with the equation of hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ we get, a = 5 and b = 2 (v)...

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### Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in the following cases: conjugate axis is 7 and passes through the point (3, -2)

conjugate axis is $7$and passes through the point $\left( 3,\text{ }-2 \right)$ Given: Conjugate axis $=\text{ }7$ Passes through the point $\left( 3,\text{ }-2 \right)$ Conjugate axis is...

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### Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in the following cases: (i) the distance between the foci = 16 and eccentricity = √2 (ii) conjugate axis is 5 and the distance between foci = 13

(i) the distance between the $foci\text{ }=\text{ }16\text{ }and\text{ }eccentricity\text{ }=\text{ }\surd 2$ Given: Distance between the foci $=\text{ }16$ Eccentricity $=\text{ }\surd 2$ Let...

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### Find the centre, eccentricity, foci and directions of the hyperbola x^2 – 3y^2 – 2x = 8

${{x}^{2}}-\text{ }3{{y}^{2}}-\text{ }2x\text{ }=\text{ }8$ Given: The equation $=>\text{ }{{x}^{2}}-\text{ }3{{y}^{2}}-\text{ }2x\text{ }=\text{ }8$ Let us find the centre, eccentricity,...

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### Find the eccentricity, coordinates of the foci, equations of directrices and length of the latus-rectum of the hyperbola. (i) 4x^2 – 3y^2 = 36 (ii) 3x^2 – y^2 = 4

(i) $4{{x}^{2}}-\text{ }3{{y}^{2}}~=\text{ }36$ Given: The equation $=>\text{ }4{{x}^{2}}-\text{ }3{{y}^{2}}~=\text{ }36$ The equation can be expressed as: The obtained equation is of the...

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### Find the eccentricity, coordinates of the foci, equations of directrices and length of the latus-rectum of the hyperbola. (i) 9×2 – 16y2 = 144 (ii) 16×2 – 9y2 = -144

(i) $9{{x}^{2}}-\text{ }16{{y}^{2}}~=\text{ }144$ Given: The equation $=>\text{ }9{{x}^{2}}-\text{ }16{{y}^{2}}~=\text{ }144$ The equation can be expressed as: The obtained equation is of the...

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