Q118 / 160 · AP EAMCET 2022 (08 Jul Shift 1) · Mathematics

The equation of the family of curves for which length of the sub normal at any point $(\mathrm{x}, \mathrm{y})$ is always a constant $(\mathrm{k})$ is

A
$y^2=4 a x$
Correct answer
B
$\mathrm{y}^2-\mathrm{A}=2 \mathrm{Kx}$
C
$y^2-K=2 x$
D
$y^2=K(x+K)$

Solution

Length of subnormal is $(\mathrm{y}, \mathrm{m})=\mathrm{k}$ $\begin{aligned} & \mathrm{y} \frac{\mathrm{dy}}{\mathrm{dx}}= \pm \mathrm{k} \\ & \mathrm{ydy}= \pm \mathrm{kdx} \\ & \frac{\mathrm{y}^2}{2}= \pm \mathrm{kx} \\ & \mathrm{y}^2= \pm 2 \mathrm{kx}+\mathrm{A} \\ & \mathrm{y}^2-\mathrm{A}= \pm 2 \mathrm{kx}\end{aligned}$

Hence, the correct answer is option: 'B'.

Relevant Questions

Every curve represented by the general solution of cuts every curve represented by the general solution of at angle . Then,06 Jul, 2022 (E)Applications of DE
At any point x , y on a curve if the length of the subnormal is x - 1 and the curve passes through 1 , 2 then the curve is a conic. A vertex04 Jul, 2022 (M)Applications of DE
Let x and y be the sides of two squares such that y = x - x 2 . The rate of change of area of the second square with respect to the area of 19 Aug, 2021 (E)Applications of DE
The radius of a circle is increasing at a rate of . Then the rate of change of area, when its radius is , is .........22 Sep, 2020 (M)Applications of DE
If it is mentioned that for a curve passing through , the slope of the curve at any point is the reciprocal, of twice the ordinate of that p22 Sep, 2020 (M)Applications of DE
If the increase in the side of square is , then the approximate percentage increase in its area ......22 Sep, 2020 (E)Applications of DE