Find the coordinates of the points of intersection of x^2/16 + y^2/25 =1 and the line with equation 5x = 4y.
thanks in advance
2007-01-25 20:07:13 · 4 answers · asked by PonkieD 1 in Science & Mathematics ➔ Mathematics
The first equation is that of a ellipse centered at (0,0)
The second equation is a line through the origin.
There are different ways of getting the intersection. It's somewhat of a matter of taste. A trial and error approach is simply and effective
guess x -> y (from line) , compare with y from ellipse
x, y
4, 5 1+1 > 1, so x is too large
1/2, 5/8 > 1/(4*16) + 25/(8^2*25) = 1/64 + 1/64 < 1 , x too small
Now you know that the solution has 1/2
I'll use my TI-83
I get x=0.7845 and y=0.9806
because of symmetery there's also an intersection at the negative of both of these.
2007-01-25 20:23:54 · answer #1 · answered by modulo_function 7 · 0⤊ 0⤋
Solve the second equation for y: y = 5x/4. Substitute that into the ellipse equation, and solve that for x. You'll get x = 4, if my mental arithmetic was accurate. Then figure out y, since you know y = 5x/4
2007-01-25 20:20:37 · answer #2 · answered by John D 3 · 0⤊ 0⤋
That's simple. Just solve for the x and y values using simultaneous equations.
2007-01-25 20:16:27 · answer #3 · answered by Anonymous · 0⤊ 1⤋
dunno
2007-01-25 20:10:14 · answer #4 · answered by Anonymous · 0⤊ 1⤋