The point on the curve y^2 = 8x for which the abscissa and ordinate change at the same rate, is Option 1: (2, -4) Option 2: (2, 4) Option 3: (1, 2√2) Option 4: (1, -2√2)

Answer: (2, 4). Solution: The abscissa (x-coordinate) and ordinate (y-coordinate) change at the same rate means: dx/dt = dy/dt where t represents time. Given the curve y^2 = 8x, differentiate both sides with respect to time t: 2y * dy/dt = 8 * dx/dt Since dx/dt = dy/dt, substitute: 2y * dx/dt = 8 * dx/dt Dividing both sides by dx/dt: 2y = 8 y = 4 Substitute y = 4 into the curve equation y^2 = 8x: (4)^2 = 8x 16 = 8x x = 2 Therefore, the point is (2, 4).

Calculus

Application of Derivatives

Medium

core

The point on the curve $y^2 = 8x$ for which the abscissa and ordinate change at the same rate, is

$(2, -4)$

$(2, 4)$

$(1, 2\sqrt{2})$

$(1, -2\sqrt{2})$

✅ Correct Option: 2

The abscissa (x-coordinate) and ordinate (y-coordinate) change at the same rate means:

$\frac{dx}{dt} = \frac{dy}{dt}$

where $t$ represents time.

Given the curve $y^2 = 8x$ , differentiate both sides with respect to time $t$ :

$2y \cdot \frac{dy}{dt} = 8 \cdot \frac{dx}{dt}$

Since $\frac{dx}{dt} = \frac{dy}{dt}$ , substitute:

$2y \cdot \frac{dx}{dt} = 8 \cdot \frac{dx}{dt}$

Dividing both sides by $\frac{dx}{dt}$ :

$2y = 8$

$y = 4$

Substitute $y = 4$ into the curve equation $y^2 = 8x$ :

$(4)^2 = 8x$

$16 = 8x$

$x = 2$

Therefore, the point is $(2, 4)$ .

2022: 23 Aug Shift 1

The position of Sumit when Amit will hit the paper ball is :

2026: 18 May Shift 1

The function $f(x) = \frac{4x^2+1}{x}$ is decreasing in

(A). $\left(\frac{-1}{2}, \frac{1}{2}\right)$

(B). $\left(-\infty, \frac{-1}{2}\right)$

(C). $\left(0, \frac{1}{2}\right)$

(D). $\left(\frac{-1}{2}, 0\right)$

Choose the correct answer from the options given below:

2026: 14 May Shift 2

For the function $f(x)=x^4-2x^2+5, x\in R$ , then which of the following statements are True?

A. $f(x)$ is increasing on $(-\infty,-1)$

B. $f(x)$ is decreasing on $(-\infty,-1)$

C. $f(x)$ is increasing on $(-1,0)\cup(1,\infty)$

D. $f(x)$ is decreasing on $(1,\infty)$

Choose the correct answer from the options given below:

2026: 29 May Shift 2

Function $f(x)=\sin3x, x \in \left[0,\frac{\pi}{2}\right]$ is decreasing in the interval

2025: 21 May Shift 1

The real valued function $f(x) = x^{15} + 5x^9 + 10$ is increasing for___________.

2025: 2 June Shift 1

The function $f(x) = 2\log_e(x-2) - x^2 + 4x + 1, (x > 2)$ is increasing on the interval:

The point on the curve y2=8xy^2 = 8xy2=8x for which the abscissa and ordinate change at the same rate, is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The point on the curve $y^2 = 8x$ for which the abscissa and ordinate change at the same rate, is