Q2 of 5 Page 781

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

Given: Parabolic reflector is 5 cm deep & its diameter is 20 cm


Need to find: Distance of its focus from the vertex.



Reflector is 5 cm deep, i.e., OD = 5 cm


Diameter of the mirror is 20 com, i.e., BC = 20 cm


Let, the equation of the parabola is y2 = 4ax, where a is the distance of the focus from the vertex.


The x-coordinate of the points B and C is 5.


D is the middle point of BC which is upon the x-axis.


So, we can say that BD = CD = 10 cm.


So, the coordinate of the point B is (5, 10)


Putting the values of the equation,


y2 = 4ax


⇒ 100 = 4a x 5


⇒ 20a = 100


⇒ a = 5


That means, the focus is 5 cm far from the vertex.


More from this chapter

All 5 →
1

The focus of a parabolic mirror is at a distance of 6 cm from its vertex. If the mirror is 20 cm deep, find its diameter.

 13

The towers of bridge, hung in the form of a parabola, have their tops 30 m above the roadway, and are 200 m apart. If the cable is 5 m above the roadway at the center of the bridge, find the length of the vertical supporting cable, 30 m from the center.

 4

A rod of length 15 cm moves with its ends always touching the coordinate axes. Find the equation of the locus of a point P on the rod, which is at a distance of 3 cm from the end in contact with the x-axis.

 5

A beam is supported at its ends by supports which are 12 m apart. Since the load is concentrated at its center, there is a deflection of 3 cm at the center, and the deflected beam is in the shape of a parabola. How far from the center is the deflection 1 cm?