The line x plus 7y=5 cuts the circle x^2 plus y^2=15 at the points P & Q. Find: a) P & Q. b) the midpoint of PQ.
(I don't know why, but the plus sign does not show after I submit d question so dats y I wrote it in words)
An identical previous post been answered.
The disappearance of the + sign is because you have probably have copied and pasted, and the original + sign was not in ASCII code if it was in another application.
If you have to cut and paste, try to first paste it in an ascii editor, such as notepad, check that everything is ok or make necessary corrections, then paste it to your post.
(Word gives me this: A+B )
I was d one dat posted d previous question, I had to re-post again cos d plus sign won't show after I click submit
Another possible reason is that your keyboard code has a different value for the "+" sign, which is rare.
To find the points of intersection (P and Q) between the line x + 7y = 5 and the circle x^2 + y^2 = 15, we can solve the system of equations.
a) Finding the points P and Q:
Step 1: Solve the linear equation x + 7y = 5 for x in terms of y:
x = 5 - 7y
Step 2: Substitute this expression for x into the equation of the circle:
(5 - 7y)^2 + y^2 = 15
Step 3: Simplify and solve for y:
25 - 70y + 49y^2 + y^2 = 15
50y^2 - 70y + 10 = 0
5y^2 - 7y + 1 = 0
Step 4: Factor the quadratic equation:
(5y - 1)(y - 1) = 0
Step 5: Solve for y:
5y - 1 = 0 or y - 1 = 0
y = 1/5 or y = 1
Step 6: Substitute the values of y back into the equation x = 5 - 7y to find x:
For y = 1/5:
x = 5 - 7(1/5) = 5 - 7/5 = 25/5 - 7/5 = 18/5
For y = 1:
x = 5 - 7(1) = 5 - 7 = -2
Therefore, the points of intersection are:
P: (18/5, 1/5)
Q: (-2, 1)
b) To find the midpoint of PQ, use the formula for the midpoint:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Let's substitute the coordinates of P and Q into this formula:
Midpoint = ((18/5 - 2) / 2, (1/5 + 1) / 2)
Midpoint = (14/5 / 2, 6/5 / 2)
Midpoint = (14/10, 6/10)
Midpoint = (7/5, 3/5)
Therefore, the midpoint of PQ is (7/5, 3/5).