Question

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis

Answer 1

Given : parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis

To find : Equation of parabola

Solution:

equation of a parabola  whose axis is along x-axis

x = a(y−k)² + h,  where (h,k) are the coordinates of the vertex.

h = 0    , k  = 0

=> x = ay²  

it passes through  (2 , 3)

=> 2 = a3²  

=> 2=9a

=> a = 2/9

x =  (2/9)y²  

=> 2y² = 9x

2y² = 9x tis he equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis

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Answer 2

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Centre = (0, 0), and major axis that passes through the points (3, 2) and (1, 6).

We know that the equation of the ellipse will be of the form when the centre is at (0, 0) and the major axis is on the y-axis,

(x^2/b^2) + (y^2/a^2) = 1 …. (1)

Here, a is the semi-major axis.

It is given that, the ellipse passes through the points (3, 2) and (1, 6).

Hence, equation (1) becomes

(9/b^2) + (4/a^2) = 1 …(2)

(1/b^2) + (36/a^2) = 1 …(3)

Solving equation (2) and (3), we get

b^2 = 10 and a^2 = 40

Therefore, the equation of the ellipse becomes: (x^2/10) + (y^2/40) = 1

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