For the equation ax^2 + 2hxy + 3y^2 + 4x + 8y | vedclass

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(A) The general equation of a second-degree curve is given by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$. For this equation to represent a circle,two co

Vedclass · Accepted Answer

$a = 3, h = 0$

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(A) The general equation of a second-degree curve is given by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$. For this equation to represent a circle,two conditions must be satisfied: $1$. The coefficient of $x^2$ must be equal to the coefficient of $y^2$,which implies $a = b$. $2$. The coefficient of the $xy$ term must be zero,which implies $h = 0$. Given the equation $ax^2 + 2hxy + 3y^2 + 4x + 8y - 6 = 0$,we compare the coefficients with the general form. Here,$b = 3$. Therefore,for the equation to represent a circle,we must have $a = 3$ and $h = 0$.

For the equation $ax^2 + 2hxy + 3y^2 + 4x + 8y - 6 = 0$ to represent a circle,what must be the values of $a$ and $h$?

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