If the equation px^2 + (2 - q)xy + 3y^2 - 6qx | vedclass

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(C) For a general second-degree equation $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ to represent a circle,two conditions must be satisfied:$1$. The coeffic

Vedclass · Accepted Answer

$3, 2$

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(C) For a general second-degree equation $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ to represent a circle,two conditions must be satisfied:$1$. The coefficient of $xy$ must be zero,so $B = 0$.$2$. The coefficients of $x^2$ and $y^2$ must be equal,so $A = C$.Given the equation $px^2 + (2 - q)xy + 3y^2 - 6qx + 30y + 6q = 0$:From condition $1$,the coefficient of $xy$ is $(2 - q) = 0$,which gives $q = 2$.From condition $2$,the coefficient of $x^2$ must equal the coefficient of $y^2$,so $p = 3$.Thus,the values are $p = 3$ and $q = 2$.

If the equation $px^2 + (2 - q)xy + 3y^2 - 6qx + 30y + 6q = 0$ represents a circle,then the values of $p$ and $q$ are:

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