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Find the eccentricity of the hyperbola.

Answer (Detailed Solution Below)

Option 4 :
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Detailed Solution

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Concept:

A standard form of the hyperbola is, 

= 1, whose eccentricity (e) = 

Calculation:

Given:

a2 = cosec2 α  and b2 = sec2 α 

We know that, 

b2 = a2 (e2 - 1)

sec2 α  = cosec2 α (e2 - 1)

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More Eccentricity of a conic Questions

Q1.The eccentricity of the conic represented by 4x2 + 9y2 = 36:-
Q2.Find the eccentricity of conic x2 + 2x + 2y2 + 4y - 13 = 0 is . 
Q3.If the distance from the focus is 12 units and the distance from the directrix is 12 units, then eccentricity = ?
Q4.Find the eccentricity of the hyperbola\(\rm \frac{x^2}{cosec^2\alpha } - \frac{y^2}{\sec^2\alpha } = 1\).
Q5.In an ellipse, the distance between its foci is 4 and minor axis is 6.Then its eccentricity is
Q6.If e and e' are eccentricities of a hyperbola and it's conjugate, then find the value of \(\rm {1\over e^2} +{1\over {e'}^{2}} \).
Q7.Consider the following with regard to eccentricity (e) of a conic section: 1. e = 0 for circle 2. e = 1 for parabola 3. e < 1 for ellipse Which of the above statements is/are correct?
Q8.What is the eccentricity of 7x2 -  9y2 = 63 ?
Q9.Eccentricity of hyperbola \(\frac{{{{\rm{x}}^2}}}{{16}} - \frac{{{{\rm{y}}^2}}}{9} = 1\)
Q10.Find the eccentricity of the ellipse 2x2 + 3y2 = 6.

More Parabola, Ellipse and Hyperbola Questions

Q1.Consider the points P(4k, 4k) and Q(4k, -4k) lying on the parabola y2 = 4kx. If the vertex is A, then what is ∠PAQ equal to?
Q2.The foci of the ellipse 4x2 + 9y2 = 1 are at Q and R. If P(x, y) is any point on the ellipse, then what is PQ + PR equal to?
Q3.The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a moving point of the parabola, is another parabola whose directrix is
Q4.If y = mx + 4 is a tangent to both the parabolas, y2 = 4x and x2 = 2by, then b is equal to
Q5.If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is
Q6.If P is a point on the parabola y = x2 + 4 which is closest to the straight line y = 4x − 1, then the co-ordinates of P are :
Q7.Let the line 2x + 3y – k = 0, k > 0, intersect the x-axis and y-axis at the points A and B, respectively. If the equation of the circle having the line segment AB as a diameter is x2 + y2 – 3x – 2y = 0 and the length of the latus rectum of the ellipse x2 + 9y2 = k2 is \(\frac{m}{n}\) , where m and n are coprime, then 2m + n is equal to
Q8. Let R be the focus of the parabola y2 = 20x and the line y = mx + c intersect the parabola at two points P and Q. Let the point G(10, 10) be the centroid of the triangle PQR. If c – m = 6, then (PQ)2 is 
Q9.Let PQ be a chord of the parabola y2 = 12x and the midpoint of PQ be at (4, 1). Then, which of the following point lies on the line passing through the points P and Q ?
Q10.Consider a hyperbola H having centre at the origin and foci and the x - axis. Let C1 be the circle touching the hyperbola H and having the centre at the origin. Let C2 be the circle touching the hyperbola H at its vertex and having the centre at one of its foci. If areas (in sq. units) of C1 and C2 are 36π and 4π, respectively, then the length (in units) of latus rectum of H is  
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