Chapter 2.2, Problem 1AYU

The intercepts of the equation $x^2+4y^2=16$ are _______. (pp. 18-19)

To determine

To fill: The intercepts of the equation $x^2 + 4y^2 = 16$ are _______.

Answer to Problem 1AYU

Solution:

$\left(0, 2\right), \left(0, -2\right)\left(4, 0\right)\text{and} \left(-4, 0\right)$

Explanation of Solution

To find $x\text{-intercept}$ put $y=0$.

$x^2=16$

$x=\pm 4$

Therefore $x\text{-intercepts}$ are $\left(4, 0\right), \left(-4, 0\right)$.

To find $y\text{-intercept}$ put $x=0$.

$4y^2=16$

$y^2=4$

$y=\pm 2$

Therefore $y\text{-intercepts}$ are $\left(0, 2\right), \left(0, -2\right)$.