Posted by **sonu** on Monday, August 8, 2011 at 10:18am.

An equitorial triangles is inscribed in the parabola y^2=4ax, where one vertex is vertex of parabola. what will be the length of the side of triangle?

- math -
**Reiny**, Monday, August 8, 2011 at 2:55pm
Never heard of an "equitorial" triangle.

Did you mean equilateral ?

I will assume you did.

let P(x,y) be the point of contact , the the other is Q(x,-y)

but y^2 = 4ax, then x = y^2/(4a)

(0,0) is the vertex of the parabola, so (0,0) must be the third point of the equilateral triangle.

From P to the origin is

√( y^2 + y^4/(16a^2))

and PQ = 2y

so

√( y^2 + y^4/(16a^2)) = 2y

( y^2 + y^4/(16a^2) = 4y^2

y^4/(16a^2) = 3y^2

y^4= 48a^2y^2

y^2= 48a^2

y = ± a√48

= ±4a√3

since PQ = 2a

each of the sides is 8a√3

## Answer This Question

## Related Questions

- maths - An equilateral triangle is inscribed in parabola y^2=4axsuch that the ...
- Math - A rectangle is inscribed between the x-axis and the parabola y=9-x^2 with...
- math - A parabola has the equation y = 4(x-3)^2-7 Choose 2 true statements: A) ...
- math - A parabola has the equation y = 4(x-3)^2-7 Choose 2 true statements: A) ...
- Algebra 1 parabola's - I have a graph with a parabola on it and asked to write ...
- algebra - 6. Find the equation of each parabola described below. a) parabola ...
- ALGEBRA 1 - Please check for me.Without drawing the graph of the given equation ...
- ALGEBRA 1 - Please check for me.Without drawing the graph of the given equation ...
- Algebra - The vertex of a parabola represented by f(x)=x^2-4x+3 has coordinates...
- Math - 1.) If a = 2 and the vertex of a parabola is (3, -4), will there be a ...

More Related Questions