I need help with these problems. If you could explain the steps/show work, it would be greatly appreciated! Thanks!
1.) A tangent line of a parabola is a line that intersects but does not cross the parabola. Prove that a line tangent to the parabola x^2=4py at the point (a, b) crosses the y-axis at (0,-b)
2.) The orbit of the moon around the earth is an ellipse with earth at one focus. If the length of the major axis of the orbit is 477,736 miles and the length of the minor axis is 477,078, find the minimum and maximum distance between the earth and the moon.
3.) April and Marty, 2 miles apart, are talking on the phone when lightning strikes nearby. They each hear the thunder, but April hears it 2.4 seconds after Marty. Sketch a graph of the locations where the lightning could have struck. (Sound travels at 1100 ft/sec). The graph should be a hyperbola.
--I know you can't show me a graph, but if you know how to make it, what points to plot, what it'd look like, it would be greatly appreciated.
4.) Graph the following equations using your graphing calculator.
a.) 9x^2+24xy+16y^2+90x-130y=0
b.) 11x^2-24xy+4y^2+30x+40y=45
-- I need help solving these equations. I need to have them solved for y=...... so I can plug it into my calculator.
Thank you so much!
1.) A tangent line of a parabola is a line that intersects but does not cross the parabola. Prove that a line tangent to the parabola x^2=4py at the point (a, b) crosses the y-axis at (0,-b)
2.) The orbit of the moon around the earth is an ellipse with earth at one focus. If the length of the major axis of the orbit is 477,736 miles and the length of the minor axis is 477,078, find the minimum and maximum distance between the earth and the moon.
3.) April and Marty, 2 miles apart, are talking on the phone when lightning strikes nearby. They each hear the thunder, but April hears it 2.4 seconds after Marty. Sketch a graph of the locations where the lightning could have struck. (Sound travels at 1100 ft/sec). The graph should be a hyperbola.
--I know you can't show me a graph, but if you know how to make it, what points to plot, what it'd look like, it would be greatly appreciated.
4.) Graph the following equations using your graphing calculator.
a.) 9x^2+24xy+16y^2+90x-130y=0
b.) 11x^2-24xy+4y^2+30x+40y=45
-- I need help solving these equations. I need to have them solved for y=...... so I can plug it into my calculator.
Thank you so much!