Question:
The equation $y^2 + 3 = 2(2x + y)$ represents a parabola with the vertex at
The equation $y^2 + 3 = 2(2x + y)$ represents a parabola with the vertex at
Updated On: Jun 17, 2022
- $\left(\frac{1}{2}, 1\right)$ and axis parallel to y-axi
- $\left(1,\frac{1}{2}\right)$ and axis parallel to x-axis
- $\left(\frac{1}{2}, 1\right)$ and focus at $\left(\frac{3}{2}, 1\right)$
- $\left(1,\frac{1}{2}\right)$ and focus at $\left(\frac{3}{2}, 1\right)$
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The Correct Option is C
Solution and Explanation
The given equation can be rewritten as
$\left(y-1\right)^{2}=4\left(x-\frac{1}{2}\right)$ which is a parabola
with its $vertex\left(\frac{1}{2}, 1\right)$ axis along the line
$y = 1$, hence axis parallel to x-axis.
Its focus is $\left(\frac{1}{2}+1, 1\right)$, i.e., $\left(\frac{3}{2}, 1\right)$
$\left(y-1\right)^{2}=4\left(x-\frac{1}{2}\right)$ which is a parabola
with its $vertex\left(\frac{1}{2}, 1\right)$ axis along the line
$y = 1$, hence axis parallel to x-axis.
Its focus is $\left(\frac{1}{2}+1, 1\right)$, i.e., $\left(\frac{3}{2}, 1\right)$
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Concepts Used:
Differential Equations
A differential equation is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point. It is mainly used in fields such as physics, engineering, biology and so on.
Orders of a Differential Equation
First Order Differential Equation
The first-order differential equation has a degree equal to 1. All the linear equations in the form of derivatives are in the first order. It has only the first derivative such as dy/dx, where x and y are the two variables and is represented as: dy/dx = f(x, y) = y’
Second-Order Differential Equation
The equation which includes second-order derivative is the second-order differential equation. It is represented as; d/dx(dy/dx) = d2y/dx2 = f”(x) = y”.
Types of Differential Equations
Differential equations can be divided into several types namely
- Ordinary Differential Equations
- Partial Differential Equations
- Linear Differential Equations
- Nonlinear differential equations
- Homogeneous Differential Equations
- Nonhomogeneous Differential Equations