MHTCET 16 Apr 2026 Shift 1 Paper

Concept:Eliminate the arbitrary constants $a$ and $b$ to form the differential equation, then find the power of the highest-order derivative.Explanation:Given equation is$$(y-a)^{2}=4(x-b)$$Differentiate both sides with respect to $x$:$$2(y-a)\frac{dy}{dx}=4$$$$(y-a)\frac{dy}{dx}=2$$Differentiate again with respect to $x$:$$\left(\frac{dy}{dx}\right)^{2}+(y-a)\frac{d^{2}y}{dx^{2}}=0$$From the first derivative result,$$y-a=\frac{2}{\frac{dy}{dx}}$$Substitute this into the second derivative equation:$$\left(\frac{dy}{dx}\right)^{2}+\frac{2}{\frac{dy}{dx}}\cdot \frac{d^{2}y}{dx^{2}}=0$$Multiplying throughout by $\frac{dy}{dx}$, we get$$\left(\frac{dy}{dx}\right)^{3}+2\frac{d^{2}y}{dx^{2}}=0$$The highest-order derivative is $\frac{d^{2}y}{dx^{2}}$, and its power is $1$.Answer:Degree is $1$.Correct option: A. 1