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Question

The coordinates of the focus of the parabola described parametrically by x=5t2+2,y=10t+4 are:


A

(7,4)

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B

(3,4)

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C

(3,-4)

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D

(-7,4)

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Solution

The correct option is A

(7,4)


Explanation for the correct option:

Given that : x=5t2+2,y=10t+4

Now solving it,

x=5t2+2x-2=5t2t2=x-25...(i)

Now, y=10t+4t=y-410....(ii)

Squaring equation (ii) and equating with (i)

y-42100=x-25y-42=20x-2

Let X=x-2&Y=y-4

Y2=20XY2=45X

Therefore, coordinate of focus is, (5,0)

As we know that if the equation of parabola is y2=4axthen the coordinate of the focus is (a,0)

Now

x-2=5x=7y-4=0y=4

Hence the required coordinates are (7,4)

Hence, option (A) is the correct answer.


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