verify that the given point is on the curve and find the lines that are a. tangent and b. normal to the…

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
Answer
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.