Question

An arch in the shape of a parabola has the equation 2y^2 -5x =0.find the co ordinates of its vertex and focus

Answer 1

SOLUTION

GIVEN

An arch in the shape of a parabola has the equation 2y² - 5x = 0.

TO DETERMINE

The coordinates of its vertex and focus

EVALUATION

Here the given equation of parabola is

2y² - 5x = 0

Which can be rewritten as

$\displaystyle \sf{2 {y}^{2} = 5x}$

$\displaystyle \sf{ \implies \: {y}^{2} = \frac{5}{2} x}$

Comparing with the general equation of the parabola y² = 4ax we get

$\displaystyle \sf{\: 4a = \frac{5}{2} }$

$\displaystyle \sf{ \implies \: a = \frac{5}{8} }$

Hence coordinates of vertex is (0,0)

Also coordinates of focus

$\displaystyle \sf{ = \bigg( \frac{5}{8} \: ,\: 0 \bigg) }$

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