## Question

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.

### Solution

32

We have *b*^{2 }= *a*^{2}(*e*^{2} – 1) = *a*^{2} ⇒ *b = a*

Also 2*ae* = 16

Hence the equation of the required hyperbola is

#### SIMILAR QUESTIONS

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 (x_{1}, y_{1}). Then is equal to –

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 –

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

For what value of *c* does not line *y* = 2*x* + *c* touches the hyperbola 16*x*^{2} – 9*y*^{2} = 144?

Determiner the equation of common tangents to the hyperbola and .

Find the locus of the mid-pints of the chords of the circle *x*^{2} – *y*^{2} = 16, which are tangent to the hyperbola 9*x*^{2} – 16*y*^{2} = 144.

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

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.

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

Find the center, eccentricity, foci and directrices of the hyperbola

16*x*^{2} – 9*y*^{2} + 32*x *+ 36*y* – 164 = 0