A) Statement -1 is true, Statement -2 is true. Statement -2 is correct explanation for statement-1.
B) Statement -1 is true, Statement-2 is true. Statement -2 is not correct explanation for statement-1.
C) Statement -1 is false. Statement-2 is true.
D) Statement -1 is true. Statement-2 is false.
E) Statement -1 is false. Statement-2 is true.
Correct Answer: B
Solution :
Statement I Let the equation of parabola whose axis is the axis of x and vertex at the origin is \[{{y}^{2}}=4ax\] \[2y\frac{dy}{dx}=4a\,\,\,\Rightarrow \,\,\,\frac{dy}{dx}=\frac{2a}{y}\] \[\Rightarrow \] \[\frac{dy}{dx}\propto \frac{1}{y}\] (where \[a\to \] parameter) Statement II \[{{y}^{2}}=4ax\] ...(i) \[\Rightarrow \] \[2y\frac{dy}{dx}=4a\]\[\Rightarrow \,\,a=\frac{y}{2}\frac{dy}{dx}\] [from Eq.(i)] \[{{y}^{2}}=4x\cdot \,\frac{y}{2}\frac{dy}{dx}\] \[\Rightarrow \] \[{{y}^{2}}=2xy\frac{dy}{dx}\] \[\Rightarrow \] \[y=2x\frac{dy}{dx}\] \[\therefore \] Order = 1 and degree = 1
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