Question:
The parabola having its focus at $(3, 2)$ and directrix along the $y$-axis has its vertex at
The parabola having its focus at $(3, 2)$ and directrix along the $y$-axis has its vertex at
Updated On: Jan 30, 2025
- (2, 2)
- $\left(\frac{3}{2} , 2 \right)$
- $\left(\frac{1}{2} , 2 \right)$
- $\left(\frac{2}{3} , 2 \right)$
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The Correct Option is B
Solution and Explanation
Vertex of the parabola is a point which lies on the axis of the parabola,
which is a line $\bot$ to the directrix through the focus,
i.e., $y = 2$ and equidistant from the focus and directrix $x = 0$,
so that the vertex is $\left(\frac{3}{2} , 2\right)$ .
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Concepts Used:
Applications of Integrals
There are distinct applications of integrals, out of which some are as follows:
In Maths
Integrals are used to find:
- The center of mass (centroid) of an area having curved sides
- The area between two curves and the area under a curve
- The curve's average value
In Physics
Integrals are used to find:
- Centre of gravity
- Mass and momentum of inertia of vehicles, satellites, and a tower
- The center of mass
- The velocity and the trajectory of a satellite at the time of placing it in orbit
- Thrust