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MATH / The points P=(x₁,y₁) and Q=(x₂,y₂) are the intersections of the parabola y²=4ax, where a>0, and a line passing through the focus of the parabola. Then the distance PQ can be expres…

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problem

The points P=(x1,y1)P = (x_1,y_1) and Q=(x2,y2)Q = (x_2,y_2) are the intersections of the parabola y2=4ax,y^2 = 4ax, where a>0,a > 0, and a line passing through the focus of the parabola. Then the distance PQPQ can be expressed in the form c1x1+c2x2+c3a,c_1 x_1 + c_2 x_2 + c_3 a, where c1,c_1, c2,c_2, and c3c_3 are constants. Compute c1+c2+c3.c_1 + c_2 + c_3.
Plain-text mathematical notation (without MathML)
The points P=(x₁,y₁) and Q=(x₂,y₂) are the intersections of the parabola y²=4ax, where a>0, and a line passing through the focus of the parabola.  Then the distance PQ can be expressed in the form c₁x₁+c₂x₂+c₃a, where c₁, c₂, and c₃ are constants.  Compute c₁+c₂+c₃.
Original LaTeX notation
The points $P = (x_1,y_1)$ and $Q = (x_2,y_2)$ are the intersections of the parabola $y^2 = 4ax,$ where $a > 0,$ and a line passing through the focus of the parabola.  Then the distance $PQ$ can be expressed in the form $c_1 x_1 + c_2 x_2 + c_3 a,$ where $c_1,$ $c_2,$ and $c_3$ are constants.  Compute $c_1 + c_2 + c_3.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
f0e02a7c-fbb3-5df9-8fb6-05b5cd59e1c2
task_key
intermediate~5falgebra--test--f0e02a7c-fbb3-5df9-8fb6-05b5cd59e1c2
task_revision_id
1
config / split
intermediate_algebra / test

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