A circle is defined by the equation given below.

1 answer:

5 0

The circle equation is in the format (x – h)2 + (y – k)2= r2, with the center being at the point (h, k) and the radius being "r".

x²+y²-8x-6y+2 =0 -----(a)
(x-4)² = x² - 8x + 16
(y-3)² = y² - 6y + 9

Equation (a) can be rewritten as:
(x-4)² + (y-3)² + 2 - 16 - 9 = 0
(x-4)² + (y-3)² = 23

The coordinates for the center of the circle is: ( 4,3)
The radius is √23=4.8

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$Let:\ x^2=t \ \ \ \ \ e^{2x}=v\\Hence,\\5t-tv+2v^2=10\\5t-tv+2v^2-10=10-10\\5t-tv-10+2v^2=0\\t(5-v)-2(5-v)=0\\(5-v)(t-2)=0\\5-v=0\\5-v+v=0+v\\5=v\\5=e^{2x}$