The point on the parabola y^2 = 18x,for which | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the point be $(x, y)$.Given that the ordinate $(y)$ is three times the abscissa $(x)$,we have $y = 3x$.Substitute $y = 3x$ into the equation o

Vedclass · Accepted Answer

$(2, 6)$

Vedclass · Answer

(D) Let the point be $(x, y)$.Given that the ordinate $(y)$ is three times the abscissa $(x)$,we have $y = 3x$.Substitute $y = 3x$ into the equation of the parabola $y^2 = 18x$:$(3x)^2 = 18x$$9x^2 = 18x$$9x^2 - 18x = 0$$9x(x - 2) = 0$This gives $x = 0$ or $x = 2$.If $x = 0$,then $y = 3(0) = 0$. The point is $(0, 0)$.If $x = 2$,then $y = 3(2) = 6$. The point is $(2, 6)$.Comparing with the given options,the correct point is $(2, 6)$.

The point on the parabola $y^2 = 18x$,for which the ordinate is three times the abscissa,is

Similar Questions

At which point does the line $x + y = 1$ intersect the parabola $y = x - x^2$?

If the equation of the parabola with vertex $V \left(\frac{3}{2}, 3\right)$ and the directrix $x + 2y = 0$ is $\alpha x^2 + \beta y^2 - \gamma xy - 30x - 60y + 225 = 0$,then $\alpha + \beta + \gamma$ is equal to:

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

If a parabola passes through the points $(-2, 1)$,$(1, 2)$,and $(-1, 3)$ and has a horizontal axis,then the length of the latus rectum of that parabola is:

The length of the latus rectum of the parabola whose focus is $(3, 3)$ and directrix is $3x - 4y - 2 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module