Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XI  >>  Math  >>  Conic Sections
0 votes

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

Can you answer this question?

1 Answer

0 votes
The problem can be diagrammatically represented as follows:
Since its a parabola opening upwards,its equation is $x^2 = 4ay$.
The parabola passes through the point $ (\large\frac{5}{2}$$,10)$
Therefore, $\large(\frac{5}{2})^2 $$=4\times a \times 10 \rightarrow a = \large\frac{5}{32}$
Therefore, the equation of the parabola is $x^2 = 4\times\large\frac{5}{32}$$\times y = \large\frac{5y}{8}$
We have to solve for $y=2m \rightarrow x^2 = \large\frac{5 \times 2}{8}$$ \rightarrow x = \large\sqrt {\frac{5}{4}}$
$\qquad AB = 2x = 2 \large\sqrt {\frac{5}{4}}$$ \approx 2.23m$
answered Apr 8, 2014 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App