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Rotate the coordinate axes to remove the xy- term, then identify the type of conic and sketch its graph. Find its focus in xy coordinate. x² + 5y² + 25xy − 6x + 2y + 20 = 0

Rotate the coordinate axes to remove the xy- term, then identify the type of conic and sketch its graph. Find its focus in xy coordinate. x² + 5y² + 25xy − 6x + 2y + 20 = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Rotate the coordinate axes to remove the xy- term, then identify the type of conic and sketch its graph. Find its focus in xy coordinate. х? + 5у? + 25ху — 6х + 2у + 20 3D 0 2. a) Find the vector component (orthogonal projection) of p =< -1, 2, 5 > along q =< 1,–1,2 > and orthogonal to q. b) Find the area of the triangle with verticesP1(5, –1, –1), P2(2, –1,–-1) andP3(1,–2,–1). c) Determine whether the vectors lie in the same plane p =< 1,5, 0 >, q =< -2,0,6 >,r =< 0,–7,1 >.
Transcribed Image Text:Rotate the coordinate axes to remove the xy- term, then identify the type of conic and sketch its graph. Find its focus in xy coordinate. х? + 5у? + 25ху — 6х + 2у + 20 3D 0 2. a) Find the vector component (orthogonal projection) of p =< -1, 2, 5 > along q =< 1,–1,2 > and orthogonal to q. b) Find the area of the triangle with verticesP1(5, –1, –1), P2(2, –1,–-1) andP3(1,–2,–1). c) Determine whether the vectors lie in the same plane p =< 1,5, 0 >, q =< -2,0,6 >,r =< 0,–7,1 >.
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