Question

S1: The differential equation of parabolas having their vertices at the origin and foci on the x-axis is an equation whose variables are separable
S2: The differential equation of the straight lines which are at a fixed distance p from the origin is an equation of degree 2
S3: The differential equation of all conics whose both axes coincide with the axes of coordinates is an equation of order 2

• A. TTT
• B. TFT
• C. FFT
• D. TTF

Answer 1

The correct option is A TTT

$S_1$ -Equation of parabola is $y^2=\pm 4ax$
$2y\frac{dy}{dx}=\pm ra$
D.E of parabola $\Rightarrow y^2=2yx\frac{dy}{dx}$
$2\frac{dy}{y}=\frac{dx}{x}$
Which is variable seperable
$S_2$ -Equation of line which is fixed distance. P from origin can be equation of tangent to circle
$s^2+y^2=p^2$
Line is $y=mx+p\sqrt{1+m^2}(m=\frac{dy}{dx})$
${(y-x\frac{dy}{dx})}^2=P(1+{\left(\frac{dy}{dx}\right)}^2)$
So, degree is 2
$S_3$ -Equation of conic whose both axis co-incide with co-ordinate axis is $a{x}^2+b{y}^2=1$
As there are two constants, so order of D.E is 2