Q. 62 - Calculus

Question

For each of the equations in Exercises 59–62, y is defined as an implicit function of x. Solve for y, and use what you find to sketch a graph of the equation.

$4y^2-x^2+25=0$

Step-by-Step Solution

Answer

The equation of $y$ is $y=\frac{\sqrt{x^2-25}}{2}$

Step 1. Given Information

The given equation is $4y^2-x^2+25=0$

Step 2. Solve for y

$$\begin{gathered} 4y^2=x^2-25 \\ {y}^2=\frac{x^2-25}{4} \\ y=\frac{\sqrt{x^2-25}}{2} \end{gathered}$$

Step 3. Graph of the Equation

We obtained $y=\frac{\pm \sqrt{x^2-25}}{2}$

The graph of hyperbola is