Question

Find the eccentricity of the hyperbola whose latus rectum is half of its transverse axis.

Solution

Correct option is

Let the equation of hyperbola 

The transverse axis = 2a and rectum.

According to the question.

                     …… (1)

We know  b2 = a2 (e2 – 1)

        

SIMILAR QUESTIONS

Q1

If a variable line  which is a chord of the hyperbola  subtends a right angle at the centre of the hyperbola then it always touches a fixed circle whose radius is – 

Q2

If values of m for which the line  touches the hyperbola 16x2 – 9y= 144 are the roots of the equation x2 –(a + b)x – 4 = 0, then value of (a + b) is equal to –

Q3

The equation of normal to the rectangular hyperbola xy = 4 at the point P on the hyperbola which is parallel to the line

2x – y = 5 is –

Q4

A tangent to the hyperbola  meets ellipse x2 + 4y2 = 4 in two distinct points. Then the locus of midpoint of this chord is –

Q5

From a point on the line y = x + c, c(parameter), tangents are drawn to the hyperbola  such that chords of contact pass through a fixed point (x1, y1). Then  is equal to –

Q6

If the portion of the asymptotes between centre and the tangent at the vertex of hyperbola  in the third quadrant is cut by the line  being parameter, then –

   

Q7

For what value of c does not line y = 2x + c touches the hyperbola 16x2 – 9y2 = 144?

Q8

Determiner the equation of common tangents to the hyperbola  and .

Q9

Find the locus of the mid-pints of the chords of the circle x2 – y2 = 16, which are tangent to the hyperbola 9x2 – 16y2 = 144.

Q10

Find the locus of the poles of the normal of the hyperbola .