For what point of the parabola the ${y^2} = 18x$ ordinate equal to three times the abscissa?

Question

Vedantu Content Team · Accepted Answer

Hint: Substitute the relation between abscissa and ordinate into the given parabola equation.

As, we know that we are given with the parabola
${y^2} = 18x$ …………………………………………………….. (1)
We know that abscissa is the x-coordinate and ordinate is the y-coordinate.
Let the abscissa and ordinate of the point on parabola be \[{x_1}\] and \[{y_1}\] respectively.
So, according to the given condition. Ordinate of the point will be equal to three times the abscissa i.e. \[{y_1} = 3{x_1}\].
So, as the points lie on the parabola the coordinates of the points must satisfy the equation of parabola.
Now substituting the coordinates of the points in equation (1) we get,
$
   \Rightarrow {y_1}^2 = 18{x_1} \\
  \Rightarrow {\left( {3{x_1}} \right)^2} = 18{x_1} \\
   \Rightarrow {9x_1}\left( {{x_1} - 2} \right) = 0 \\
   \Rightarrow {x_1} = 0,2 \\
$
Hence,
For ${x_1} = 0 \Rightarrow {y_1} = 0$, Point$\left( {0,0} \right)$
For ${x_1} = 2 \Rightarrow {y_1} = 6$, Point$\left( {2,6} \right)$
Note: Whenever we come across these types of problems then we have to remember that if a point lies on the curve then its coordinates must satisfy the equation of the curve.

For what point of the parabola the ${y^2} = 18x$ ordinate equal to three times the abscissa?

NCERT Book Solutions

Reference Book Solutions

Question Papers

Exams

Quick Links

For what point of the parabola the ${y^2} = 18x$ ordinate equal to three times the abscissa?

Book your FREE Online counselling session

Your FREE Online counselling session has been booked!

Please try again later

NCERT Book Solutions

Reference Book Solutions

Question Papers

Exams

Quick Links