## Question

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

### Solution

Let vertex be (*a*, 0) and focus (*ae*, 0) then

Again *b*^{2 }= *a*^{2}(*e*^{2} – 1) = 3*a*^{2}

The equation of hyperbola is

#### SIMILAR QUESTIONS

A tangent to the hyperbola meets ellipse x^{2} + 4y^{2} = 4 in two distinct points. Then the locus of midpoint of this chord is –

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 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.