The maximum value of x 2+y 2 is the equation: (x+1) 2+(y-1) 2 = 3 2 represents the maximum distance from the point on the circumference to the coordinate origin. The intersection of a straight line and a circle obtained by connecting the coordinate origin and the center (-1, 1), where one is the smallest and the other is the largest.
The maximum value is: distance from origin to center (-1, 1)+ radius = √ (- 1) * (- 1)+3 = 3+. √.
The maximum value of x 2+y 2 is 1 1+6√2.
The minimum value is: distance from origin to center (-1, 1)- radius = √ (-1) * (-1)+1*)-3 = 3-. √ 2.
The maximum value of x 2+y 2 is 1 1-6√2.
The second question: Like the first question, find the distance from the center of the circle to the point (4,3) and then add the radius to get the maximum value and subtract the radius to get the minimum value.
Question 3: Find the distance from the center to the straight line first, and the absolute value is 3 * (1)+4 *1-2518.
—————————— = —— =3.6
Root number 3 2+4 2 5
Subtract the radius to get the minimum value, 3.6-3=0.6 or 3/5.
Let p(x 1, y 1) be substituted into a straight line: 3x 1+4y 1-25=0, that is, 25-4y 1.
x 1=—————
three
P(x 1, y 1), substituted into the circle: (x1+1) 2+(y1-1) 2 = 3 2.
The two equations are simultaneous and x 1 is solved. Finally, you can solve y 1 by substituting into the first equation, and finally you can find point p.