Question

Vertex of the parabola 2y2 + 3y + 4x -2 = 0 is​

Answer 1

Answer:

Correct option is (A) (2532-74

Answer 2

SOLUTION

TO DETERMINE

The Vertex of the parabola

$\displaystyle \sf{2 {y}^{2} + 3y + 4x - 2 = 0}$

EVALUATION

Here the given equation of the parabola is

$\displaystyle \sf{2 {y}^{2} + 3y + 4x - 2 = 0}$

Which can be rewritten as

$\displaystyle \sf{2 {y}^{2} + 3y + 4x - 2 = 0}$

$\displaystyle \sf{ \implies \: {y}^{2} + \frac{3}{2} y + 2x - 1 = 0}$

$\displaystyle \sf{ \implies \: {y}^{2} + 2.\frac{3}{4}. y + { \bigg( \frac{3}{4} \bigg )}^{2} - { \bigg( \frac{3}{4} \bigg )}^{2} + 2x - 1 = 0}$

$\displaystyle \sf{ \implies \: { \bigg( y + \frac{3}{4} \bigg )}^{2} - \frac{9}{16} + 2x - 1 = 0}$

$\displaystyle \sf{ \implies \: { \bigg( y + \frac{3}{4} \bigg )}^{2} = - 2x + \frac{9}{16} + 1 }$

$\displaystyle \sf{ \implies \: { \bigg( y + \frac{3}{4} \bigg )}^{2} = - 2x + \frac{25}{16} }$

$\displaystyle \sf{ \implies \: { \bigg( y + \frac{3}{4} \bigg )}^{2} = - 2 \bigg(x + \frac{25}{32} \bigg ) }$

Hence the required vertex is

$\displaystyle \sf{ \bigg( - \frac{25}{32} , - \frac{3}{4} \bigg ) }$

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