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

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Question

(C) For the general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ to represent a circle,the following conditions must be satisfied:$

Vedclass · Accepted Answer

$3, 2$

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(C) For the general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ to represent a circle,the following conditions must be satisfied:$1$. The coefficient of $x^2$ must be equal to the coefficient of $y^2$ $(a = b)$.$2$. The coefficient of $xy$ must be zero $(h = 0)$.Given the equation $px^2 + (2 - q)xy + 3y^2 - 6qx + 30y + 6q = 0$:Comparing the coefficients:Coefficient of $x^2$ is $p$ and coefficient of $y^2$ is $3$.Setting $p = 3$.Coefficient of $xy$ is $(2 - q)$.Setting $2 - q = 0$,we get $q = 2$.Therefore,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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