What is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are x+y=0 and x-y=0?
- A. x^{2}+y^{2}=1
- B. x^{2}+y^{2}=25 ✓
- C. x^{2}+y^{2}=100
- D. x^{2}+y^{2}-2x-2y-23=0
Correct Answer: B. x^{2}+y^{2}=25
Explanation
The center of the circle is the intersection of its diameters, x+y=0 and x-y=0, which is (0,0). The diameter is 10, so the radius is r = 5. The equation of the circle is (x-0)^2 + (y-0)^2 = 5^2 \implies x^2+y^2=25.
Related questions on Analytical Geometry (2D)
- Consider the following statements in respect of the line passing through origin and inclining at an angle of 75^{\circ} with the positive ...
- If P(3,4) is the mid-point of a line segment between the axes, then what is the equation of the line ?
- The base AB of an equilateral triangle ABC with side 8 cm lies along the y-axis such that the mid-point of AB is at the origin and B...
- The centre of the circle passing through origin and making positive intercepts 4 and 6 on the coordinate axes, lies on the line
- The centre of an ellipse is at (0,0), major axis is on the y-axis. If the ellipse passes through (3,2) and (1,6), then what is its ecc...