Question:
If the circle \(S_1 = x^2 + y^2 + 2gx + 4y + 1 = 0\) bisects the circumference of circle \(x^2 + y^2 - 2x - 3 = 0\), then the radius of circle \(S_1\) is
If the circle \(S_1 = x^2 + y^2 + 2gx + 4y + 1 = 0\) bisects the circumference of circle \(x^2 + y^2 - 2x - 3 = 0\), then the radius of circle \(S_1\) is
Show Hint
Use geometric constraints like bisection to infer positional relation and derive radius.
Updated On: Jun 4, 2025
- \(5\)
- \(\sqrt{12}\)
- \(25\)
- \(12\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
If it bisects circumference, then it must pass through extremities of diameter of given circle. Use this and center-radius form to get radius of \(S_1\)
Was this answer helpful?
0
0
Top Questions on Geometry
- Let the volume of a metallic hollow sphere be constant. If the inner radius increases at the rate of 2 cm/s, find the rate of increase of the outer radius when the radii are 2 cm and 4 cm respectively.
- The equation of the normal drawn at the point \((\sqrt{2}+1, -1)\) to the ellipse \(x^2 + 2y^2 - 2x + 8y + 5 = 0\) is
- Surface area of a balloon (spherical), when air is blown into it, increases at a rate of 5 mm²/s. When the radius of the balloon is 8 mm, find the rate at which the volume of the balloon is increasing.
- A cylindrical water container has developed a leak at the bottom. The water is leaking at the rate of 5 cm$^3$/s from the leak. If the radius of the container is 15 cm, find the rate at which the height of water is decreasing inside the container, when the height of water is 2 meters.
- The coordinates of the foot of the perpendicular drawn from the point $A(-2, 3, 5)$ on the y-axis are:
View More Questions
Questions Asked in AP EAPCET exam
- If a steel rod of a radius 10 mm and length 80 cm is streched by a force of 66 kN along its length, then the longitudinal stress on the rod is nearly
- AP EAPCET - 2025
- mechanical properties of solids
- The number of all five-letter words (with or without meaning) having at least one repeated letter that can be formed by using the letters of the word INCONVENIENCE is:
- AP EAPCET - 2025
- Binomial Expansion
- If \(\alpha, \beta, \gamma\) are the roots of the equation \[ x^3 - 13x^2 + kx + 189 = 0 \] such that \(\beta - \gamma = 2\), then find the ratio \(\beta + \gamma : k + \alpha\).
- In a container of volume 16.62 m$^3$ at 0°C temperature, 2 moles of oxygen, 5 moles of nitrogen and 3 moles of hydrogen are present, then the pressure in the container is (Universal gas constant = 8.31 J/mol K)
- AP EAPCET - 2025
- Ideal gas equation
- If \[ A = \begin{bmatrix} x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1 \end{bmatrix}, \] where \( x \) and \( y \) are non-zero real numbers, trace of \( A = 0 \), and determinant of \( A = -6 \), then the minor of the element 1 of \( A \) is:}
- AP EAPCET - 2025
- Complex numbers
View More Questions