Question

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

Answer 1

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)

Answer 2

Answer:(5,0)

Step-by-step explanation:

A parabolic reflector with diameter PR=20 cm and OQ=5cm

Vertex of parabola is (0,0)

Let the focus of parabola be (a,0)

Now ,

You may see ,

PR=20 cm

=1/2×PR=PQ= 10 cm

Coordinates of point p are (5,10)

Since this point lies on the parabola

y²=4ax

=>10²=5×4a

=>a=5

So, required focus of parabola is(5,0)