5272道题目5525 条题源记录 · 相同内容已合并
圆・圆的方程与切线挑战
A circle in the xy-plane has its center at \( (-7,\ 3) \) and has a radius of 9. An equation of this circle is \( x^2+y^2+ax+by+c=0 \), where a, b, and c are constants. What is the value of c ?
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圆・圆的方程与切线进阶
Circles A and B are graphed in the xy-plane. Circle A is represented by the equation \( \left(x+8\right)^2+\left(y-8\right)^2=64 \) and intersects the x-axis at the point (r, s). Circle B has its center at (r, s) and has a radius of the same length as circle A. Which equation represents circle B?
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圆・圆的方程与切线挑战
A circle in the xy-plane has its center at \( (2,\ 9) \). Line t is tangent to this circle at the point \( (a,−4) \), where a is a constant. The slope of line t is \( \frac{6}{5} \). What is the value of a?
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圆・圆的方程与切线进阶
\( x^2+52x+y^2=0 \)
In the xy-plane, the graph of the given equation is a circle. What are the coordinates \( (x,\ y) \) of the center of the circle?
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圆・圆的方程与切线挑战
A circle in the xy-plane has its center at \( (2,\ 7) \). Line t is tangent to this circle at the point \( (a,−4) \), where a is a constant. The slope of line t is \( \frac{6}{5} \). What is the value of a?
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圆・圆的方程与切线挑战
In the figure shown, points A, B, C, and E lie on the circle, and AB<BC. Segment AC is perpendicular to segment BE at point D, and BD=DE=\( \sqrt{398} \). The diameter of the circle is 201. If \( \frac{CD}{AD}=r \) what is the value of \( r \)?
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圆・圆的方程与切线挑战
In the xy-plane, an equation of circle A is \( (x-3)^2+(y-9)^2=25 \) . Circle B has the same center as circle A but has a radius that is twice the radius of circle A. Which equation represents circle B?
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圆・圆的方程与切线挑战
A circle in the xy-plane has its center at (-5, 2) and the point (-9, 5) lies on the circle. Which equation represents this circle?
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圆・圆的方程与切线进阶
A circle in the xy-plane has its center at (−4, 1) and the point (−8, 4) lies on the circle. Which equation represents this circle?
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圆・圆的方程与切线进阶
What is the radius of the circle in the xy-plane defined by \( (x+3)^2+(y+9)^2=361 \) ?
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圆・圆的方程与切线挑战
A circle has center P, and points A and B lie on the circle. The measure of arc AB is 45° and the length of arc AB is \( 4π \) units. What is the length, in units, of the radius of the circle?
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圆・圆的方程与切线挑战
\( x^2+y^2=36 \)
\( y=mx+\frac{b}{4} \)
In the given system of equations, m and b are negative constants. In the xy-plane, the graphs of the equations in the given system intersect at the point \( (-5,\ y) \), where \( y<0 \). Which expression represents the value of b?
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