1. Let k be a positive real number. The line x+y=k and the circle x2+y2=k are drawn. Find k so that the line is tangent to the circle.
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2. A circle passes through the points (−2,0), (2,0), and (3,2). Find the center of the circle. Enter your answer as an ordered pair.
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Thank you!
+659 One question per post please.
1. This is mostly geometry believe it or not.
The value of K in the circle equation would be the blue line squared. Or in other words, the blue line is √k
The value of BC in the tangent equation would just be k
We know ABC is a 45 - 45 - 90 triangle (If the coefficients of x and y are 1 when graphed in standard form for the red line). The blue line is the perpendicular bisector.
Based on pythagorean theorem: 2∗√k2=k2 (two legs are √k and hypotenuse is BC)
2k=k2
k(k−2)=0
k=2
