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. 2x² - √5xy + y² = 6, (√5,4). the point is on the curve because when is substituted for x and is substituted for y, the resulting statement is = 6, which is a statement. (simplify your answers.) false true

Explanation:

Step1: Substitute x and y values

Substitute $x = \sqrt{5}$ and $y = 4$ into $2x^{2}-\sqrt{5}xy + y^{2}$.
$2(\sqrt{5})^{2}-\sqrt{5}\times\sqrt{5}\times4+4^{2}$

Step2: Simplify the expression

First, calculate each term:
$2\times5 - 5\times4+16$
$10-20 + 16$
$6$

Answer:

The point is on the curve because when $\sqrt{5}$ is substituted for $x$ and $4$ is substituted for $y$, the resulting statement is $6 = 6$, which is a true statement.