Question

The order and the degree of the differential equation of all tangent lines to the parabola $x^2=4y$ is:

• A. $2,1$
• B. $2,2$
• C. $1,3$
• D. $1,4$

Answer 1

Answer: (A)

$2,1$

$\frac{x^2}{4}=y$
$\Rightarrow \frac{dy}{dx}=\frac{x}{2}$
$\Rightarrow (y-k)=\frac{dy}{dx}(x-h)$
$\Rightarrow 2(y-k)=x^2-hx$
differentiating both sides with respect to x,
$\Rightarrow 2y_1=2x-h$
$\Rightarrow 2y_2=2$
$\Rightarrow y_2=1$
$Order=2$
$degree=1$