Question

verify that the given point is on the curve and find the lines that are a. tangent and b. normal to the curve at the given point. $x^{2}+y^{2}=18,(3, - 3)$ the point is on the curve because when is substituted for x and is substituted for y, the resulting statement is = 18, which is a statement. (simplify your answers.)

Explanation:

Step1: Verify the point on the curve

Substitute $x = 3$ and $y=-3$ into the equation $x^{2}+y^{2}$.
$3^{2}+(-3)^{2}=9 + 9$

Step2: Calculate the result

$9+9=18$
Since $18 = 18$, the statement is true.

Answer:

The point is on the curve because when $3$ is substituted for $x$ and $- 3$ is substituted for $y$, the resulting statement is $18=18$, which is a true statement.