If a parabolic reflector is 20 cm in diameter

Asked by admin @ 13/08/2021 in Math viewed by 291 People

Question 1 If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

Class X1 - Maths -Conic Sections Page 264

Answered by admin @ 13/08/2021

Let vertex of parabola is at origin. axis of parabola is along the X-axis. so, the equation of parabola is y² = 4ax . so, focus is (a, 0)

A/C to question,
Depth is 5 cm , diameter is 20 cm.
see attachment ,
it is clear that point P( 5, 10)
∵ point P( 5, 10) lies on parabola.
∴ ( 10)² = 4 × a × 5
a = 5

here,
focus is the midpoint of given diameter .
so, S = ( 5 , 0)

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