$ { ext{Write an equation of the horizontal parabola with the given vertex and passing through the given point}}{ ext{.}} \ { ext{Vertex at }}\left( { - 8,2} ight){ ext{ and passing through }}\left( {2, - 3} ight). \ $

Question

$    {	ext{Write an equation of the horizontal parabola with the given vertex and passing through the given point}}{	ext{.}}   \  {	ext{Vertex at }}\left( { - 8,2} ight){	ext{ and passing through }}\left( {2, - 3} ight).   \ $

Vedantu Content Team · Accepted Answer

$   {	ext{As you know that general equation of a horizontal parabola is:}}   \  {\left( {y - k} ight)^2} = 4a\left( {x - h} ight){	ext{             }}   \  {	ext{As Vertex is given to us as }}\left( { - 8,2} ight){	ext{, therefore we have}}   \  {\left( {y - 2} ight)^2} = 4a\left( {x - \left( { - 8} ight)} ight){	ext{             }}   \   \Rightarrow {\left( {y - 2} ight)^2} = 4a\left( {x + 8} ight){	ext{            }} - Equation(1){	ext{     }}   \  {	ext{Now, putting }}\left( {2, - 3} ight){	ext{ in Equation(1) we get}}   \  {\left( { - 3 - 2} ight)^2}{	ext{ }} = {	ext{ }}4a\left( {2 + 8} ight)   \   \Rightarrow {\left( { - 5} ight)^2}{	ext{ }} = {	ext{ }}4a\left( {10} ight){	ext{             }}   \   \Rightarrow 25 = 40a   \   \Rightarrow a = \frac{5}{8}{	ext{                                }} - Equation(2)   \  {	ext{Using Equation(2) in Equation(1)}}   \   \Rightarrow {\left( {y - 2} ight)^2} = 4\left( {\frac{5}{8}} ight)\left( {x + 8} ight)   \   \Rightarrow {\left( {y - 2} ight)^2} = \frac{5}{2}\left( {x + 8} ight){	ext{ is the required Equation}}   \  {	ext{Note: For these kinds of questions we must remember the general equation of a horizontal }}   \  {	ext{parabola and then put vertex's coordinates in it to get the equation in only one variable 'a'}}{	ext{. }}   \  {	ext{Now, Put the coordinates if the point given to be on the parabola and solve to get value of 'a'}}{	ext{. }}   \  {	ext{Put the value of 'a' in the equation to get desired equation}}{	ext{.}}   \ $

$

{\text{Write an equation of the horizontal parabola with the given vertex and passing through the given point}}{\text{.}} \\
{\text{Vertex at }}\left( { - 8,2} \right){\text{ and passing through }}\left( {2, - 3} \right). \\
$

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$ {\text{Write an equation of the horizontal parabola with the given vertex and passing through the given point}}{\text{.}} \\ {\text{Vertex at }}\left( { - 8,2} \right){\text{ and passing through }}\left( {2, - 3} \right). \\ $

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