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AP EAMCET · Maths · Differential Equations

If it is mentioned that for a curve passing through \((3,4)\), the slope of the curve at any point is the reciprocal, of twice the ordinate of that point, then that curve is a

  1. A Ellipse
  2. B Parabola
  3. C Hyperbola
  4. D Circle
Verified Solution

Answer & Solution

Correct Answer

(B) Parabola

Step-by-step Solution

Detailed explanation

According to given information the slope of curve at point \((x, y)\) is \[ \frac{d y}{d x}=\frac{1}{2 y} \Rightarrow \int 2 y d y=\int d x \] \[ \Rightarrow \quad y^2=x+c \] \(\because\) Curve (i) passes through point \((3,4)\), so \(c=13\). \(\therefore\) Required curve…