﻿ 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. : Kaysons Education

# 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.

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## Question

### 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

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Q2

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Q3

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Q4

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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.