7x2 - 4xy + 7y² - 25 = 0 (a) Identify the resulting rotated conic. O ellipse parabola O hyperbola (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
7x2 - 4xy + 7y² - 25 = 0 (a) Identify the resulting rotated conic. O ellipse parabola O hyperbola (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
7x2 - 4xy + 7y² - 25 = 0 (a) Identify the resulting rotated conic. O ellipse parabola O hyperbola (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
Transcribed Image Text:Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation.
7x2 - 4xy + 7y² - 25 = 0
(a) Identify the resulting rotated conic.
ellipse
parabola
O hyperbola
(b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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