x^2 = - 6y at (6,-6)
cuts the parabola again at X
fine the coordinates of X
cuts the parabola again at X
fine the coordinates of X
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x² = -6y
(x - 0)² = 4(-3/2)(y - 0), standard form
The focus of the parabola is (0, -3/2).
The chord includes points (6, -6) and (0, -3/2). Find the equation of the chord.
slope = (-6 + 3/2) / (6 - 0) = -3/4
y-intercept = -3/2
y = -(3/4)x - 3/2
Substitute that into the parabola equation.
x² = -6[-(3/4)x - 3/2]
x² = (9/2)x + 9
2x² - 9x - 18 = 0
(2x + 3)(x - 6) = 0
x = -3/2 or x = 6
These are the x-coordinates of the points of intersection of the parabola and the chord. The second one was given in the problem, so use the first solution and substitute it into the equation of the chord.
y = -(3/4)(-3/2) - 3/2
y = -3/8
The other end of the chord is (-3/2, -3/8).
(x - 0)² = 4(-3/2)(y - 0), standard form
The focus of the parabola is (0, -3/2).
The chord includes points (6, -6) and (0, -3/2). Find the equation of the chord.
slope = (-6 + 3/2) / (6 - 0) = -3/4
y-intercept = -3/2
y = -(3/4)x - 3/2
Substitute that into the parabola equation.
x² = -6[-(3/4)x - 3/2]
x² = (9/2)x + 9
2x² - 9x - 18 = 0
(2x + 3)(x - 6) = 0
x = -3/2 or x = 6
These are the x-coordinates of the points of intersection of the parabola and the chord. The second one was given in the problem, so use the first solution and substitute it into the equation of the chord.
y = -(3/4)(-3/2) - 3/2
y = -3/8
The other end of the chord is (-3/2, -3/8).
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If y = -6, x^2 = -6(-6) = 36
x = ± 6
The other point is (-6, -6)
x = ± 6
The other point is (-6, -6)