Focus coordinates of straight line 3x + 10y-25 = 0, ellipse x2 / 25 + Y2 / 4 = 1 Is to find the coordinates of the intersection point

Focus coordinates of straight line 3x + 10y-25 = 0, ellipse x2 / 25 + Y2 / 4 = 1 Is to find the coordinates of the intersection point

Idea: substituting the linear equation y = (25-3x) / 10 into the elliptic equation, we can get
The quadratic equation of one variable about X is solved, and then x is obtained. Finally, the corresponding y is calculated according to the linear equation,
Finally (x, y) is the intersection coordinates

What is the distance from the right intersection of ellipse x ^ 2 / 16 + y ^ 2 / 9 = 1 to the straight line y = 3x?

x^2/16+y^2/9=1
a=4,b=3
C = root 7
The distance from the right focus (root 7,0) to the line y = 3x is 3 root (70) / 10

X to y = 1:5 / 3, y to Z = 5:6, x + Z equals 27

X to y = 1 to 5 / 3
x=3/5*y
Y is better than z = 5 to 6
z=6/5*y
Substitute x + Z = 27 to get
3/5*y+6/5*y=27
9/5*y=27
y=27*5/9
y=15
therefore
x=9
z=18