Find the equation of the parabola that satisfies the following conditions: Vertex \((0, 0)\), passing through \((5, 2) \)and symmetric with respect to the y-axis
Given that, the vertex is \((0, 0)\) and the parabola is symmetric about the \(y-axis\),
the equation of the parabola is either of the form \(x^2= 4ay\) or \(x^2= -4ay. \)
The parabola passes through the point \((5, 2)\), which lies in the first quadrant.
Therefore, the equation of the parabola is of the form \(x^2= 4ay\), while point \((5, 2)\) must satisfy the equation \(x^2= 4ay\)
\(∴ 5^2 = 4a(2)\)
\(25 = 8a\)
\(a = \dfrac{25}{8}\)
Thus, the equation of the parabola is
\(x^2 = 4 (\dfrac{25}{8})y\)
\(x^2 = \dfrac{25y}{2}\)
\(2x^2 = 25y\)
∴ The equation of the parabola is \(2x^2 = 25y\) (Ans.)
Figures 9.20(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
Parabola is defined as the locus of points equidistant from a fixed point (called focus) and a fixed-line (called directrix).
=> MP2 = PS2
=> MP2 = PS2
So, (b + y)2 = (y - b)2 + x2