Question

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. 11) xy+16=0 A) θ=45∘

B) θ=45∘ y²/32+x²/32= 1 y²/32-x²/32= 1 ellipse hyperbola center at (0,0) center at (0,0) major axis is y'-axis transverse axis is y'-axis vertices at (0,±4√2)vertices at(0,±4√2) C) θ=45∘ D) θ=36.9∘ y'²=-32x' parabola x²/4+y²/2=1 vertex at (0,0) ellipse focus at (−8,0) center at (0,0) major axis is the x' -axis vertices at (±2,0)

Answer 1

To rotate the axes so that the new equation contains no xy-term, we can use the rotation transformation equations. The new equation after rotating the axes is an ellipse with certain properties.

Step-by-step explanation:

To rotate the axes so that the new equation contains no xy-term, we need to find the angle of rotation (θ). From the given options, θ is either 45∘ or 36.9∘. Let's assume θ=45∘.

To rotate the given equation xy+16=0, we can use the rotation transformation equations: x' = x*cos(θ) - y*sin(θ) and y' = x*sin(θ) + y*cos(θ).

Substituting the values, we have x'y' + 16*cos(θ) = 0 or y'²/32 + x'²/32 = 1. So, the new equation after rotating the axes is an ellipse centered at (0,0), with the major axis along the y'-axis and vertices at (0,±4√2).