john458776
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- May 15, 2021
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I'm really confused how I can approach this problem. Give me hints then I'll solve it and send the solution here. Please guide me and teach me.
The center will be 5 units from each intercept. You can solve geometrically or algebraically; take your pick. If you draw the diagram right, you may be able to solve it mentally.I'm really confused how I can approach this problem. Give me hints then I'll solve it and send the solution here. Please guide me and teach me.
The center will be 5 units from each intercept. You can solve geometrically or algebraically; take your pick. If you draw the diagram right, you may be able to solve it mentally.
Of course, there are two such circles.
I suppose you meant \(\displaystyle r^2=(x_1-x_2)^2+(y_1-y_2)^2\).Okay, I tried finding x using the distance formular.
Okay, I tried finding x using the distance formular.
Okay I get it now.The x-value of the circle center is midway between the x-values of the two x-intercepts ...
So the center of the circle is \((-1,k)\). Find \(k\) so that the center is \(5\) units to each of the intercepts.Let's use the midpoint formular to find x-intercept
xm[MATH] = ([/MATH]x2[MATH]+[/MATH]x1)/2
xm[MATH]=[/MATH][MATH](2+(-4))[/MATH]/2
xm[MATH]=-1[/MATH]
[MATH](x-a)[/MATH]2[MATH]+[/MATH][MATH](x-k)[/MATH]2[MATH]=[/MATH]52So the center of the circle is \((-1,k)\). Find \(k\) so that the center is \(5\) units to each of the intercepts.
Both are correct. As Prof. Peterson told you there are two circles that have intercepts \((-4,0)~\&~(2,0)\) with radius \(5\).[MATH]k=4[/MATH] or [MATH]k=-4[/MATH]This is correct right ?
Which one is the y-intercept of center between [MATH]-4[/MATH] or [MATH]4[/MATH]
Have you tried a drawing yet?[MATH](x-a)[/MATH]2[MATH]+[/MATH][MATH](x-k)[/MATH]2[MATH]=[/MATH]52
[MATH](2 ; 0)[/MATH]
[MATH](2+1)[/MATH]2[MATH]+[/MATH][MATH](0-k)[/MATH]2[MATH]=25[/MATH][MATH]9+[/MATH][MATH]k[/MATH]2[MATH]=25[/MATH][MATH]k=4[/MATH] or [MATH]k=-4[/MATH]
This is correct right ?
Which one is the y-intercept of center between [MATH]-4[/MATH] or [MATH]4[/MATH]