﻿ 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. : Kaysons Education

# 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.

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## Question

### Solution

Correct option is

32

We have ba2(e2 – 1) = a2  ⇒ b = a

Also     2ae = 16

Hence the equation of the required hyperbola is

#### SIMILAR QUESTIONS

Q1

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 –

Q2

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 –

Q3

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

Q4

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

Q5

Determiner the equation of common tangents to the hyperbola  and .

Q6

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.

Q7

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

Q8

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.

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 center, eccentricity, foci and directrices of the hyperbola

16x2 – 9y2 + 32+ 36y – 164 = 0