Question

Obtain the equation of a hyperbola with coordinate axes as principal axes given that the distance of one of its vertices from the foci are 9 and 1 units.

Solution

Correct option is

If vertices are A(a, 0) and A’(–a, 0) and foci are S’(–ae, 0)

Given  l (S’A) = 9 and l (SA) = 1

⇒        a + ae = 9 and ae – a = 1

Or     a(1 + e) = 9 and or a(e – 1) = 1

    

∴             a(1 + e) = 9

     

⇒         a = 4

           b2 = a2(e2 – 1)

                  

∴         b2 = 9

From (1), equation of hyperbola is

          

 

SIMILAR QUESTIONS

Q1

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

Q2

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 –

Q3

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 –

   

Q4

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

Q5

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

Q6

Determiner the equation of common tangents to the hyperbola  and .

Q7

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.

Q8

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

Q9

Find the equation to the hyperbola of given transverse axes whose vertex bisects the distance between the center and the focus.

Q10

Find the equation of the hyperbola, the distance between whose foci is 16, whose eccentricity is  and whose axis is along the x-axis with the origin as its center.