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Question

A conic section is defined by the equations x = - 1 + sect y = 2 + z tant. The coordinates of the foci are,


A

(110,2) and (1+10,2)

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B

(18,2) and (1+8,2)

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C

(1,28) and (1,2+8)

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D

(1,210) and (1,2+10)

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Solution

The correct option is A

(110,2) and (1+10,2)


The parametric form of the conic section is given as (-1+sec t,2+3 tant)=(x,y).

i.e,sect=x+1,tant=(y2)3

We know

sec2ttan2t=1

Eliminating from this form,

(x+1)2[y23]2=1

This is a hyperbola with origin at (-1,2)

a2=1

b2=9

e2=1+b2a2=1+9

=10

Coordinates of focus=(±ae1,0+2)

(±101,+2)

foci are (1+10,2) and (110,2)


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