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

Question

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

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

Answer 1

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

Compare with

$ax^2+bxy+cy^2+dx+ey+f=0\\ a=5; b = -24; c=-5; d=4; e= 58; f=-59\\ Now \\ b^2-4ac\\ (-24)^2-4*5*(-5)= 676\\ b^2-4ac > 0 \\ Hence \space \space a \space hyperbola \\ The \space equation \space is \\ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\ \frac{x^2}{5^2}-\frac{y^2}{(-24)^2}=1\\ \frac{x^2}{25}-\frac{y^2}{576}=1\\$