A parabolic reflector is 5 cm deep and its diameter is 20 cm. How far

1.	A parabolic reflector is 5 cm deep and its diameter is 20 cm. How far is its focus from the vertex?
Answer» Reflector depth = OD = 5 cm Diameter of the mirror = BC = 20 cm Consider the equation of the parabola is y² = 4ax To find : Length of a, which is distance of the focus from the vertex. Since parabolic reflector is 5 cm deep, which shows x-coordinate of the points B and C is 5. Again, BD = CD = 10 cm [D is the middle point of BC] Therefore, coordinate of B is (5, 10) Point B lies on the parabolic reflector, which means it satisfy the equation y² = 4ax 100 = 20a or a = 5

A parabolic reflector is 5 cm deep and its diameter is 20 cm. How far is its focus from the vertex?

Answer»

Reflector depth = OD = 5 cm

Diameter of the mirror = BC = 20 cm

Consider the equation of the parabola is y² = 4ax

To find : Length of a, which is distance of the focus from the vertex.

Since parabolic reflector is 5 cm deep, which shows x-coordinate of the points B and C is 5.

Again, BD = CD = 10 cm

[D is the middle point of BC]

Therefore, coordinate of B is (5, 10)

Point B lies on the parabolic reflector, which means it satisfy the equation y² = 4ax

100 = 20a

or a = 5