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
- A Ellipse
- B Parabola
- C Hyperbola
- D Circle
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…
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