## Question

### Solution

Correct option is

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

Again   ba2(e2 – 1) = 3a2

The 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

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.

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.