Let the eccentricity of the hyperbola
\(H : \frac{x²}{a²} - \frac{y²}{b²} = 1\)
be √(5/2) and length of its latus rectum be 6√2, If y = 2x + c is a tangent to the hyperbola H. then the value of c2 is equal to
Let the eccentricity of the hyperbola
\(H : \frac{x²}{a²} - \frac{y²}{b²} = 1\)
be √(5/2) and length of its latus rectum be 6√2, If y = 2x + c is a tangent to the hyperbola H. then the value of c2 is equal to
18
20
24
32
The Correct Option is B
Solution and Explanation
The correct answer is (B) : 20
\(1 + \frac{b²}{a²} = \frac{5}{2} ⇒ \frac{b²}{a²} = \frac{3}{2}\)
\(\frac{2b²}{a} = 6\sqrt2 = 2 . \frac{3}{2} . a = 6\sqrt2\)
\(⇒ a = 2\sqrt2 , b² = 12\)
\(c² = a²m² - b² = 8.4 - 12 = 20\)
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Concepts Used:
Hyperbola
Hyperbola is the locus of all the points in a plane such that the difference in their distances from two fixed points in the plane is constant.
Hyperbola is made up of two similar curves that resemble a parabola. Hyperbola has two fixed points which can be shown in the picture, are known as foci or focus. When we join the foci or focus using a line segment then its midpoint gives us centre. Hence, this line segment is known as the transverse axis.
