Mathis Stuart

10/22/2023 · Elementary School

v. Find the focus and vertex of the parabola \( y^{2}=-12 x \) vi. Show that the equation \( 9 x^{2}-18 x+4 y^{2}+8 y-23=0 \) represents an ellipse. vii. Find an equation of the hyperbola with the data: Foci \( (0, \pm 6), e=2 \) viii. Write an equation of the tangent to the conic \( \frac{x^{2}}{8}+\frac{y^{2}}{9}=1 \) at the point \( \left(\frac{8}{3}, 1\right) \). ix. Find the vector from the point \( A \) to the origin where \( \overrightarrow{A B}=4 \underline{i}-2 \underline{j} \) and \( B \) is the point \( (-2,5) \). x. If \( O \) is the origin and \( \overrightarrow{O P}=\overrightarrow{A B} \), find the point \( P \) when \( A \) and \( B \) are \( (-3,7) \) and \( (1,0) \) respective xi. Define direction angles and direction cosines of a vector. xii. Find the angle between the vectors \( \underline{u}=2 \underline{i}-\underline{j}+\underline{k} \) and \( \underline{v}=-\underline{i}+\underline{j} \). iii. If \( \underline{v} \) is a vector for which \( \underline{v} \cdot \underline{i}=0, \underline{v} \cdot \underline{j}=0, \underline{v} \cdot \underline{k}=0 \) find \( \underline{v} \).