Ok so I have the question and answer but need to be explained why the answer works.
1 answer:
As you know the directrix and focus. so first of all find the distance 'a.f' shown in the figure. now find the location of the mid point of the line 'a.f' because it's the vertex. half the distance to get the focal length 'a'. now put all the values in the equation given to get the equation of required parabola.
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Answer:
(x, y) = (1, 3)
Step-by-step explanation:
The "work" of solving by graphing is typing the equations into a graphing calculator and highlighting the point of intersection.
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If you're graphing these by hand, there are a couple of strategies you can use. One is to make use of the intercepts of the line. For each of these, you need to rearrange the equation to a suitable form.
<u>3y -6 = 3x</u>
To put this into "intercept form", put the variable terms on one side of the equal sign and the constant on the other. Then divide by the constant and express the resulting variable coefficients as denominators.
3x -3y = -6
x/(-6/3) +y/(-6/-3) = 1
x/(-2) + y/2 = 1 . . . . . . The x-intercept is -2; the y-intercept is 2.
Plot the intercept points and draw a line through them.
<u>y +2x = 5</u>
The intercepts for this one are found by dividing by 5:
x/(5/2) + y/5 = 1 . . . . . . The x-intercept is 2.5; the y-intercept is 5.
The other strategy you can use for this one is to rearrange the equation to slope-intercept form and make use of those numbers.
y = -2x + 5
The y-intercept is 5 (as we already found above), and the slope is -2. That means the line drops 2 units for each unit it goes to the right. Apart from the y-intercept, other points on this line will be (1, 3), (2, 1), (3, -1).
<u>Solution</u>
When you plot these lines, you find they intersect at (1, 3). That is the solution to the system of equations, the values of x and y that satisfy both equations.
