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QJEEM24Maca71: JEE Main 2024 Mathematics - Class 11 JEEM24Maca71 Solution: Consider a circle , where . If the circle touches the line at…

Consider a circle (x−α)2+(y−β)2=50(x-\alpha)^2+(y-\beta)^2=50 , where \alpha, \beta>0 . If the circle touches the line y+x=0y+x=0 at the point PP , whose distance from the origin is 424 \sqrt{2} , then (α+β)2(\alpha+\beta)^2 is equal to __________.

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JEE Main 2024 (Online) 27th January Evening Shift Mathematics - Circle Question 23 English Explanation

amp;S:(x−α)2+(y−β)2=50amp;CP=ramp;∣α+β2∣=52amp;⇒(α+β)2=100\begin{aligned}& S:(x-\alpha)^2+(y-\beta)^2=50 \\& C P=r \\& \left|\frac{\alpha+\beta}{\sqrt{2}}\right|=5 \sqrt{2} \\& \Rightarrow(\alpha+\beta)^2=100\end{aligned}

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