Question 1186522
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{{{5x^2-4y^2-20x-24y-36=0}}}<br>
(1) group the x and y terms together; factor out the leading coefficients for both variables; move the constant to the other side:
{{{5(x^2-4x)-4(y^2+6y)=36}}}<br>
(2) complete the square in x and y, making sure to add/subtract appropriate constants on the right to keep the equation balanced:
{{{5(x^2-4x+4)-4(y^2+6y+9)=36+20-36=20}}}<br>
(3) divide by the constant on the right (to make the right side equal to 1); write the expression for each variable as a binomial square:
{{{(x-2)^2/4-(y+3)^2/5=1}}}<br>
Done....<br>