Question 450.
Determine the general equation for the parabola with its focus is located on (6,4) and that its directrix equation is 4x + y -6 = 0.
Answer 450.
Parabola is defined as a set of points equidistant from a given point, called focus and a given line, called directrix.
If P (x, y) is a point on the parabola,
its distance from the focus (6, 4) = √[(x - 6)^2 + (y - 4)^2]
and its distance from the directrix 4x + y - 6 = 0 is
l4x + y - 6l / √(4^2 + 1^2)
=> √[(x - 6)^2 + (y - 4)^2] = l4x + y - 6l / √(4^2 + 1^2)
=> 17 [(x - 6)^2 + (y - 4)^2] = (4x + y - 6)^2
=> 17 (x^2 + y^2 - 12x - 8y + 52) = (16x^2 + y^2 + 36 + 8xy - 12y - 48x)
=> x^2 + 16y^2 - 8xy - 156x - 124y + 848 = 0.
Link to YA!
Determine the general equation for the parabola with its focus is located on (6,4) and that its directrix equation is 4x + y -6 = 0.
Answer 450.
Parabola is defined as a set of points equidistant from a given point, called focus and a given line, called directrix.
If P (x, y) is a point on the parabola,
its distance from the focus (6, 4) = √[(x - 6)^2 + (y - 4)^2]
and its distance from the directrix 4x + y - 6 = 0 is
l4x + y - 6l / √(4^2 + 1^2)
=> √[(x - 6)^2 + (y - 4)^2] = l4x + y - 6l / √(4^2 + 1^2)
=> 17 [(x - 6)^2 + (y - 4)^2] = (4x + y - 6)^2
=> 17 (x^2 + y^2 - 12x - 8y + 52) = (16x^2 + y^2 + 36 + 8xy - 12y - 48x)
=> x^2 + 16y^2 - 8xy - 156x - 124y + 848 = 0.
Link to YA!
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