TS EAMCET · Maths · Differential Equations
The differential equation of the family of parabolas with vertex at \((0,-1)\) and having axis along the \(Y\)-axis is
- A \(y y^{\prime}+2 x y+1=0\)
- B \(x y^{\prime}+y+1=0\)
- C \(x y^{\prime}-2 y-2=0\)
- D \(x y^{\prime}-y-1=0\)
Answer & Solution
Correct Answer
(C) \(x y^{\prime}-2 y-2=0\)
Step-by-step Solution
Detailed explanation
Equation of family of parabola having vertex \((0,-1)\) and axis along \(y\)-axis is \[ x^2=4 a(y+1) \] On differentiating both sides w.r.t. \(x\), we get \[ 2 x=4 a y^{\prime} \Rightarrow a=\frac{x}{2 y^{\prime}} \] On putting \(a=\frac{1}{2 y^{\prime}}\) in Eq. (i), we get…
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