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MATH / The equation of the circle shown in the following diagram can be written as x²+Ay²+Bx+Cy+D=0. Find A+B+C+D. [asy] import graph; size(8.55cm); real lsf=0.5; pen dps=linewidth(0.7)+f…

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problem

The equation of the circle shown in the following diagram can be written as x2+Ay2+Bx+Cy+D=0x^2 + Ay^2 + Bx + Cy + D = 0. Find A+B+C+DA+B+C+D. [asy] import graph; size(8.55cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(8); defaultpen(dps); pen ds=black; real xmin=-3.99,xmax=4.56,ymin=-1.7,ymax=3.78; Label laxis; laxis.p=fontsize(8); xaxis("xx",xmin,xmax,defaultpen+black,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); yaxis("yy",ymin,ymax,defaultpen+black,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); draw(circle((-1,1),2.24)); dot((-1,1),ds); label("(−1,1)(-1, 1)",(-0.93,1.12),NE*lsf); dot((1,2),ds); label("(1,2)(1, 2)",(1.07,2.11),NE*lsf); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); [/asy]
Plain-text mathematical notation (without MathML)
The equation of the circle shown in the following diagram can be written as x²+Ay²+Bx+Cy+D=0. Find A+B+C+D. [asy]
import graph; size(8.55cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(8); defaultpen(dps); pen ds=black; real xmin=-3.99,xmax=4.56,ymin=-1.7,ymax=3.78;

Label laxis; laxis.p=fontsize(8);

xaxis("x",xmin,xmax,defaultpen+black,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); yaxis("y",ymin,ymax,defaultpen+black,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); draw(circle((-1,1),2.24));

dot((-1,1),ds); label("(−1,1)",(-0.93,1.12),NE*lsf); dot((1,2),ds); label("(1,2)",(1.07,2.11),NE*lsf);

clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]
Original LaTeX notation
The equation of the circle shown in the following diagram can be written as $x^2 + Ay^2 + Bx + Cy + D = 0$. Find $A+B+C+D$. [asy]
import graph; size(8.55cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(8); defaultpen(dps); pen ds=black; real xmin=-3.99,xmax=4.56,ymin=-1.7,ymax=3.78;

Label laxis; laxis.p=fontsize(8);

xaxis("$x$",xmin,xmax,defaultpen+black,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); yaxis("$y$",ymin,ymax,defaultpen+black,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); draw(circle((-1,1),2.24));

dot((-1,1),ds); label("$(-1, 1)$",(-0.93,1.12),NE*lsf); dot((1,2),ds); label("$(1, 2)$",(1.07,2.11),NE*lsf);

clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]

level

Level 5

type

Algebra

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Source and history

task_id
3d38a65c-0bbb-5b84-9188-9042c1e7a25f
task_key
algebra--test--3d38a65c-0bbb-5b84-9188-9042c1e7a25f
task_revision_id
1
config / split
algebra / test

Official source

initial import