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

$A$ pair of tangents is drawn from an external point $P$ to the parabola $y^2 = 4x$. If $\theta_1$ and $\theta_2$ are the angles made by the tangents with the $x$-axis such that $\theta_1 + \theta_2 = \frac{\pi}{4}$,find the locus of $P$.

If two perpendicular tangents are drawn from a point $P$ to the parabola $y^2 = 4x$,find the locus of $P$.

Find the coordinates of the focus,axis of the parabola,the equation of the directrix,and the length of the latus rectum for $x^{2} = -16y$.

If $ax + by = 1$ is a normal to the parabola $y^2 = 4px$, then the condition is:

If the normal to the parabola $y^2=4x$ at $P(1,2)$ meets the parabola again at $Q$,then the coordinates of $Q$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module