Q. 265.0( 2 Votes )
Find the equation of the parabola that satisfies the given conditions: Vertex (0,0) passing through (2,3) and axis is along x-axis.
Since the parabola is symmetric about x-axis and has its vertex at the origin, the equation is of the form y2 = 4ax or y2 = -4ax, where the sign depends on whether the parabola opens to the right or left. But the parabola passes through (2, 3) which lies in the first quadrant, it must open to the right. Thus the equation is of the form y2 = 4ax.
Since the parabola passes through (2, 3) we have
32 = 4a(2) ⇒ 9 = 8a ⇒ a =
Therefore, the equation of the parabola is
y2 = 4 = x ⇒ 2y2 = 9x.
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Quiz on properties of focal chord of parabola36 mins
Focal chord of parabola29 mins
Equation of tangent to parabola | Conic Section38 mins
Equation of tangent to parabola | Conic Section | Quiz1 mins
Interactive Quiz on Equation of Parabola41 mins
Lecture on Equation of Parabola59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
view all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation