Question:
If the chord joining points \((1,2)\) and \((2,-1)\) on a circle subtends an angle \(\frac{\pi}{4}\) at any point on its circumference, then the equation of such a circle is?
If the chord joining points \((1,2)\) and \((2,-1)\) on a circle subtends an angle \(\frac{\pi}{4}\) at any point on its circumference, then the equation of such a circle is?
Show Hint
Use angle subtended by chord property and general circle equation passing through chord endpoints.
Updated On: Jun 6, 2025
- \(x^2 + y^2 + 6x - 2y + 5 = 0\)
- \(x^2 + y^2 - 6x - 2y + 5 = 0\)
- \(x^2 + y^2 - 6x + 2y + 5 = 0\)
- \(x^2 + y^2 + 6x + 2y + 5 = 0\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Given chord AB between \((1,2)\) and \((2,-1)\).
Circle passes through A and B and every point on circle subtends angle \(\pi/4\) to chord AB.
Using chord length and angle subtended formula, and circle equation general form, the correct equation is
\[
x^2 + y^2 - 6x - 2y + 5 = 0.
\]
Was this answer helpful?
0
0
Top Questions on Geometry
- The equation of the circle with extremities \( (1, 3) \) and \( (5, 7) \) of the diameter is:
- A window is in the form of a rectangle surmounted by an equilateral triangle on its length. Let the rectangular part have length and breadth x and y metres respectively.
- 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.
View More Questions
Questions Asked in AP EAPCET exam
The logic gate equivalent to the combination of logic gates shown in the figure is
- AP EAPCET - 2025
- Logic gates
- In Young’s double slit experiment, the wavelengths of red and blue lights used are \(7.5 \times 10^{-5}\) cm and \(5 \times 10^{-5}\) cm respectively. If the \(n^{th}\) bright fringe of red color coincides with \((n+1)^{th}\) bright fringe of blue colour, then the value of \( n \) is
- AP EAPCET - 2025
- Polarization
- If \( \log_2 3 = p \), express \( \log_8 9 \) in terms of \( p \):
- AP EAPCET - 2025
- Exponential and Logarithmic Functions
- All the values of \(k\) such that the quadratic expression \(2kx^2 - (4k+1)x + 2\) is negative for exactly three integral values of \(x\), lie in the interval:
- If a ball projected vertically upwards with certain initial velocity from the ground crosses a point at a height of 25 m twice in a time interval of 4 s, then the initial velocity of the ball is
(Acceleration due to gravity $= 10~\text{m/s}^2$)- AP EAPCET - 2025
- Kinematics
View More Questions