Find the point on the parabola y^2 = 18x wher | vedclass

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

Question

(D) Given the equation of the parabola is $y^2 = 18x$. Differentiating both sides with respect to $t$,we get $2y \frac{dy}{dt} = 18 \frac{dx}{dt}$,whi

Vedclass · Accepted Answer

$\left( \frac{9}{8}, \frac{9}{2} \right)$

Vedclass · Answer

(D) Given the equation of the parabola is $y^2 = 18x$. Differentiating both sides with respect to $t$,we get $2y \frac{dy}{dt} = 18 \frac{dx}{dt}$,which simplifies to $y \frac{dy}{dt} = 9 \frac{dx}{dt}$ (Equation $1$). It is given that the rate of change of the $y$-coordinate is twice the rate of change of the $x$-coordinate,i.e.,$\frac{dy}{dt} = 2 \frac{dx}{dt}$. Substituting this into Equation $1$,we get $y(2 \frac{dx}{dt}) = 9 \frac{dx}{dt}$. Assuming $\frac{dx}{dt} 
eq 0$,we have $2y = 9$,which implies $y = \frac{9}{2}$. Substituting $y = \frac{9}{2}$ into the original equation $y^2 = 18x$,we get $\left( \frac{9}{2} ight)^2 = 18x$. This gives $\frac{81}{4} = 18x$,so $x = \frac{81}{4 	imes 18} = \frac{9}{8}$. Thus,the required point is $\left( \frac{9}{8}, \frac{9}{2} ight)$.

Find the point on the parabola $y^2 = 18x$ where the rate of change of the $y$-coordinate is twice the rate of change of the $x$-coordinate.

Similar Questions

The radius of a circle is increasing at the rate of $2 \text{ cm/sec}$. The rate at which its area is increasing when the radius of the circle is $5 \text{ decimeters}$ is:

If a particle moves in a straight line according to the law $x = a \sin (\sqrt{\lambda} t + b)$, then the particle will come to rest at two points whose distance is [symbols have their usual meaning]

Find the rate of change of the area of a circle with respect to its radius $r$ when $r=5 \text{ cm}$.

If the edge of a cube increases at the rate of $60 \, cm/s$,at what rate is the volume increasing when the edge is $90 \, cm$ (in $cm^3/s$)?

If $f(x) = 2x^{2}$,find $\frac{f(3.8) - f(4)}{3.8 - 4}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module