Chapter 2: Q. 1 (page 76)

The intercepts of the equation $x^{2} + 4 y^{2} = 16$ are ______________________________.

Short Answer

Expert verified

The intercepts are $(4, 0), (- 4, 0), (0, 2) and (0, - 2)$ .

Step by step solution

Step 1. Given information

The given equation is $x^{2} + 4 y^{2} = 16$ .

Need to find the intercepts of the given equation.

Step 2. Finding y-intercept

Substitute $x = 0$ in the equation $x^{2} + 4 y^{2} = 16$ and solve for yto obtain the y-intercepts.

$\begin{array}{rcl} {(0)}^{2} + 4 {(y)}^{2} & = & 16 \\ 4 y^{2} & = & 16 \\ y^{2} & = & 4 \\ y^{2} - 4 & = & 0 \\ (y - 2) (y + 2) & = & 0 \end{array}$

$y = 2 o r y = - 2$

The intercepts on the y-axis are $(0, 2)$ and $(0, - 2)$ .

Step 3. Finding x-intercept

Substitute $y = 0$ in the equation $x^{2} + 4 y^{2} = 16$ and solve for $x$ to obtain the x-intercepts.

$\begin{array}{rcl} x^{2} + 4 {(0)}^{2} & = & 16 \\ x^{2} & = & 16 \\ x^{2} - 16 & = & 0 \\ (x - 4) (x + 4) & = & 0 \end{array}$

$\begin{array}{rcl} x & = & 4 o r x = - 4 \end{array}$

The intercepts on the x-axis are $(4, 0)$ and $(- 4, 0)$ .

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The intercepts of the equation $x^{2} + 4 y^{2} = 16$ are ______________________________.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding y-intercept

Step 3. Finding x-intercept

One App. One Place for Learning.

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The intercepts of the equationx2+4y2=16 are ______________________________.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding y-intercept

Step 3. Finding x-intercept

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

The intercepts of the equation $x^{2} + 4 y^{2} = 16$ are ______________________________.