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If a parabola reflector with its axis as x-axis is 20 cm in di

Question

If a parabola reflector with its axis as $x - a x i s$ is $20$ cm in diameter and $5$ cm deep. Find the focus.

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If a parabola reflector with its axis as

x - a x i s

20

cm in diameter and

5

cm deep. Find the focus.

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

The origin of the coordinate plane is taken at the vertex of the parabolic reflector in such a way that the axis of the reflector is along the positive

x

-axis.
The equation of the parabola is of the form

y^{2} = 4 a x

(as it is opening to the right)

Given, diameter of parabola

= 20

Since, parabola is symmetric about

x

-axis.

So, co-ordinates of point

A

are

(5, 10)

Since the parabola passes through the point

A (5, 10)

1 0^{2} = 4 a (5)

\Rightarrow 100 = 20 a

\Rightarrow a = \frac{100}{20} = 5

Therefore, the focus of the parabola is

(a, 0) = (5, 0)

which is the mid-point of the diameter.

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Question Text	If a parabola reflector with its axis as $x - a x i s$ is $20$ cm in diameter and $5$ cm deep. Find the focus.
Answer Type	Text solution:1
Upvotes	150

If a parabola reflector with its axis as x−axis is 20 cm in diameter and 5 cm deep. Find the focus.

Text solutionVerified

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If a parabola reflector with its axis as $x - a x i s$ is $20$ cm in diameter and $5$ cm deep. Find the focus.