TS EAMCET · Maths · Differential Equations
If \(m\) and \(n\) are the order and degree of the differential equation of the family of parabolas with focus at the origin and \(X\)-axis as its axis, then \(m n-m+n=\)
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
Equation of family of parabola with focus at origin and the \(X\)-axis its axis is \[ \begin{aligned} & & y^2 & =-4 a(x-a) \\ \Rightarrow & & y^2 & =-4 a x+4 a^2 \\ \Rightarrow & & 2 y y^{\prime} & =-4 a \\ \Rightarrow & & a & =-\frac{y y^{\prime}}{2} \end{aligned} \] Putting…
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