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MATH / If each point of the circle x²+y²=25 is reflected in the point (4,1), the set of image points satisfies the equation x²+ay²+bx+cy+d=0.Compute the ordered quadruple (a,b,c,d) of rea…

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problem

If each point of the circle x2+y2=25x^2 + y^2 = 25 is reflected in the point (4,1),(4,1), the set of image points satisfies the equation x2+ay2+bx+cy+d=0.x^2 + ay^2 + bx + cy + d = 0.Compute the ordered quadruple (a,b,c,d)(a,b,c,d) of real numbers.
Plain-text mathematical notation (without MathML)
If each point of the circle x²+y²=25 is reflected in the point (4,1), the set of image points satisfies the equation
x²+ay²+bx+cy+d=0.Compute the ordered quadruple (a,b,c,d) of real numbers.
Original LaTeX notation
If each point of the circle $x^2 + y^2 = 25$ is reflected in the point $(4,1),$ the set of image points satisfies the equation
\[x^2 + ay^2 + bx + cy + d = 0.\]Compute the ordered quadruple $(a,b,c,d)$ of real numbers.

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
c004038d-6dda-5896-bfd4-03888c2c0308
task_key
intermediate~5falgebra--test--c004038d-6dda-5896-bfd4-03888c2c0308
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import