5272道题目5525 条题源记录 · 相同内容已合并
圆・圆的方程与切线进阶
\( (x−3)^{2}+(y−9)^{2}=6 \)
In the xy-plane, the graph of the given equation is a circle. Which point lies on this circle?
原库参考解析
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 =\( \sqrt{390} \) .The diameter of the circle is 197. If\( \frac{CD}{AD}=r \), what is the value of r ?
原库参考解析
圆・圆的方程与切线挑战
\( 2x^2+2y^2+tx+ty-78=0 \)
The given equation, where t is a positive constant, defines a circle in the xy-plane. The radius of this circle is \( \sqrt{41} \). What is the value of t?
原库参考解析
圆・圆的方程与切线进阶
In the xy-plane, the graph of the equation \( \left(x-4\right)^2+\left(y-2\right)^2=16 \) is a circle. The point \( \left(8,\ c\right) \), where c is a constant, lies on this circle. What is the value of c?
原库参考解析
圆・圆的方程与切线挑战
\( c(r)=\frac{2}{5}(2πr) \)
The function c gives the partial length, in centimeters (cm), of the circumference of a circle with a radius that measures r cm. According to the function, for each increase of 18 cm in the length of the radius, this partial length of the circumference increases by kπ cm. What is the value of k?
原库参考解析
圆・圆的方程与切线进阶
Circle A in the xy-plane has the equation \( \left(x+3\right)^2+\left(y-3\right)^2=16 \). Circle B has the same center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the xy-plane is \( \left(x+3\right)^2+\left(y-3\right)^2=k \) , where k is a constant. What is the value of k?
原库参考解析
圆・圆的方程与切线挑战
\( x^2-4x+y^2-8y-80=0 \)
In the xy-plane, the graph of the given equation is a circle. If this circle is inscribed in a square, what is the perimeter of the square?
原库参考解析
圆・圆的方程与切线进阶
A circle in the xy-plane has its center at (19, 16) and has a radius of 8k. Which equation represents this circle?
原库参考解析
圆・圆的方程与切线进阶
\( x^2-16x+y^2-10y-55=0 \)
In the xy-plane, the graph of the given equation is a circle. If this circle is inscribed in a square, what is the perimeter of the square?
原库参考解析
圆・圆的方程与切线挑战
A circle is inscribed in a square such that the circumference of the circle touches the midpoint of each side of the square. The length of the diagonal of the square is 228 units. What is the area, in square units, of the circle?
原库参考解析
圆・圆的方程与切线进阶
A circle has center O, and points A and B lie on the circle. The measure of arc AB is 20°, and the length of this arc is 4 inches. What is the circumference, in inches, of the circle?
原库参考解析
圆・圆的方程与切线进阶
What is the radius of the circle in the xy-plane defined by \( \left(x+4\right)^2+\left(y+8\right)^2=169 \)?
原库参考解析
