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}=26,(-1,5)) the point is on the curve because when (square) is substituted for x and (square) is substituted for y, the resulting statement is (square = 26), which is a (square) statement. (simplify your answers.)

Explanation:

Step1: Substitute x and y values

Substitute $x=-1$ and $y = 5$ into the equation $x^{2}+y^{2}$. So we have $(-1)^{2}+5^{2}$.

Step2: Calculate the result

$(-1)^{2}+5^{2}=1 + 25=26$. Since the result is equal to the right - hand side of the equation $x^{2}+y^{2}=26$, the statement is true.

Answer:

The point is on the curve because when $-1$ is substituted for $x$ and $5$ is substituted for $y$, the resulting statement is $26=26$, which is a true statement.