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MATH / If A=(3,4) and C=(7,10) are opposite vertices of a rectangle ABCD, then vertices A,B,C, and D must lie on the circle x²+y²−px−qy+s=0.Compute the ordered triple of real numbers …

Problem

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problem

If A=(3,4)A = (3,4) and C=(7,10)C = (7,10) are opposite vertices of a rectangle ABCD,ABCD, then vertices A,B,C,A, B, C, and DD must lie on the circle x2+y2−px−qy+s=0.x^2 + y^2 - px - qy + s = 0.Compute the ordered triple of real numbers (p,q,s).(p,q,s).
Plain-text mathematical notation (without MathML)
If A=(3,4) and C=(7,10) are opposite vertices of a rectangle ABCD, then vertices A,B,C, and D must lie on the circle
x²+y²−px−qy+s=0.Compute the ordered triple of real numbers (p,q,s).
Original LaTeX notation
If $A = (3,4)$ and $C = (7,10)$ are opposite vertices of a rectangle $ABCD,$ then vertices $A, B, C,$ and $D$ must lie on the circle
\[x^2 + y^2 - px - qy + s = 0.\]Compute the ordered triple of real numbers $(p,q,s).$

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
8ddf446b-2620-5c34-8a57-03586fe18d79
task_key
intermediate~5falgebra--test--8ddf446b-2620-5c34-8a57-03586fe18d79
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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