Q. 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.

Given: The focus of a parabolic mirror is at a distance of 6 cm from its vertex. And the mirror is 20 cm deep.

Need to find: Diameter of the mirror. Here O is the vertex and A is the Focus. So, OA = a = 6 cm.

OD is the deep of the mirror = 20 cm

BC is the diameter of the mirror.

Equation of the parabola is, y2 = 4ax

y2 = 24x

The mirror is 20 cm deep. That means the x-coordinate of the points B, C and D is 20

Both the points, B and C are on the parabola. Hence, the points satisfies the equation of the parabola.

Therefore, y2 = 24 x 20 = 480

y = 21.9

So, the coordinate of B is (20, 21.9) and the coordinate of C is (20, -21.9).

Therefore, the diameter of the mirror is = (21.9 + 21.9) cm

= 43.8 cm

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Focal chord of parabola29 mins  Quiz on properties of focal chord of parabola36 mins  Interactive Quiz on Equation of Parabola41 mins  Lecture on Equation of Parabola59 mins  Applications of +I and -I41 mins  Interactive Quiz on Algae32 mins  Lecture on Algae46 mins  Interactive Quiz on Plant Tissues52 mins  Features, similarities and dissimilarities between bryophytes and pteridophytes51 mins  How to correlate the features of multicellular algae and protists57 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 