The differential equation of all parabolas having their axis of symmetry coinciding with the axis of x has its order and degree respectively

Question

The differential equation of all parabolas having their axis of symmetry coinciding with the axis of x has its order and degree respectively (A) (2,1) (B) (2,2) (C) (1,2) (D) (1,1)

Tardigrade Admin · Accepted Answer

text equation ( x - a )2+ y 2=( x - b )2 [ S =( a , 0) ; D: x = b ] y 2=( b 2- a 2)+2 x ( a - b ) differentiate twice to get y (d2 y/d x2)+[(d y/d x)]2=0 ; y (d2 y/d xx)+((d y/d x))2=0.

Q. The differential equation of all parabolas having their axis of symmetry coinciding with the axis of $x$ has its order and degree respectively

$(2, 1)$

$(2, 2)$

$(1, 2)$

$(1, 1)$

$equation (x - a)^{2} + y^{2} = (x - b)^{2} [S = (a, 0); D : x = b]$
$y^{2} = (b^{2} - a^{2}) + 2 x (a - b)$
differentiate twice to get $y \frac{d ^{2} y}{d x ^{2}} + [\frac{d y}{d x}]^{2} = 0; y \frac{d ^{2} y}{d x ^{x}} + (\frac{d y}{d x})^{2} = 0$ .

Q. The differential equation of all parabolas having their axis of symmetry coinciding with the axis of x has its order and degree respectively

(2,1)

(2,2)

(1,2)

(1,1)