Answer to Question #221320 in Electrical Engineering for Mohsin Al Mamun

Question #221320

Identify the following conic and hence reduce it in its standard form:

5x2-24xy-5y2+4x+58y-59=0


1
Expert's answer
2021-07-30T04:05:01-0400

"5x^2-24xy-5y^2+4x+58y-59=0"

Compare with

"ax^2+bxy+cy^2+dx+ey+f=0\\\\\na=5; b = -24; c=-5; d=4; e= 58; f=-59\\\\\nNow \\\\\nb^2-4ac\\\\\n(-24)^2-4*5*(-5)= 676\\\\\nb^2-4ac > 0 \\\\\nHence \\space \\space a \\space hyperbola \\\\\nThe \\space equation \\space is \\\\\n\\frac{x^2}{a^2}-\\frac{y^2}{b^2}=1\\\\\n\\frac{x^2}{5^2}-\\frac{y^2}{(-24)^2}=1\\\\\n\\frac{x^2}{25}-\\frac{y^2}{576}=1\\\\"



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