The points of intersection of the circles x^2 | vedclass

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(B) Given equations of circles are:$x^2 + y^2 = 2ax$ ... $(i)$$x^2 + y^2 = 2by$ ... $(ii)$Subtracting $(ii)$ from $(i)$,we get:$2ax - 2by = 0 \implies

Vedclass · Accepted Answer

$(0, 0), \left( \frac{2ab^2}{a^2 + b^2}, \frac{2a^2b}{a^2 + b^2} \right)$

Vedclass · Answer

(B) Given equations of circles are:$x^2 + y^2 = 2ax$ ... $(i)$$x^2 + y^2 = 2by$ ... $(ii)$Subtracting $(ii)$ from $(i)$,we get:$2ax - 2by = 0 \implies ax = by \implies y = \frac{a}{b}x$Substituting $y = \frac{a}{b}x$ into $(i)$:$x^2 + \left( \frac{a}{b}x \right)^2 = 2ax$$x^2 + \frac{a^2}{b^2}x^2 = 2ax$$x^2 \left( 1 + \frac{a^2}{b^2} \right) = 2ax$$x^2 \left( \frac{a^2 + b^2}{b^2} \right) = 2ax$$x \left[ x \left( \frac{a^2 + b^2}{b^2} \right) - 2a \right] = 0$This gives $x = 0$ or $x = \frac{2ab^2}{a^2 + b^2}$.If $x = 0$,then $y = \frac{a}{b}(0) = 0$.If $x = \frac{2ab^2}{a^2 + b^2}$,then $y = \frac{a}{b} \left( \frac{2ab^2}{a^2 + b^2} \right) = \frac{2a^2b}{a^2 + b^2}$.Thus,the points of intersection are $(0, 0)$ and $\left( \frac{2ab^2}{a^2 + b^2}, \frac{2a^2b}{a^2 + b^2} \right)$.

The points of intersection of the circles $x^2 + y^2 = 2ax$ and $x^2 + y^2 = 2by$ are

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