Question:
The equation of the circle passing through (1, 0) and (0, 1) and having the smallest possible radius is
The equation of the circle passing through (1, 0) and (0, 1) and having the smallest possible radius is
Show Hint
The equation of the circle passing through (1, 0) and (0, 1) and having the smallest possible radius is
Updated On: Apr 15, 2026
- $x^{2}-y^{2}-x-y=0$
- $x^{2}+y^{2}-x-y=0$
- $x^{2}+y^{2}+x+y=0$
- $x^{2}+y^{2}-2x-2y=0$
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
For a circle passing through two points to have the minimum radius, the line segment joining the two points must be the diameter of the circle.
Step 2: Analysis
Using the diameter form of a circle equation $(x-x_1)(x-x_2) + (y-y_1)(y-y_2) = 0$ for points (1, 0) and (0, 1).
Step 3: Evaluation
$(x-1)(x-0) + (y-0)(y-1) = 0 \Rightarrow x^2 - x + y^2 - y = 0$.
Step 4: Conclusion
The equation is $x^2 + y^2 - x - y = 0$.
Final Answer: (b)
For a circle passing through two points to have the minimum radius, the line segment joining the two points must be the diameter of the circle.
Step 2: Analysis
Using the diameter form of a circle equation $(x-x_1)(x-x_2) + (y-y_1)(y-y_2) = 0$ for points (1, 0) and (0, 1).
Step 3: Evaluation
$(x-1)(x-0) + (y-0)(y-1) = 0 \Rightarrow x^2 - x + y^2 - y = 0$.
Step 4: Conclusion
The equation is $x^2 + y^2 - x - y = 0$.
Final Answer: (b)
Was this answer helpful?
0
0
Top MET Mathematics Questions
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- The equation $3^{3x + 4} = 9^{2x - 2},\ x>0$ has the solution
- A parallelogram is constructed on the vectors $\mathbf{a} = 3\alpha - \beta$, $\mathbf{b} = \alpha + 3\beta$. If $|\alpha| = |\beta| = 2$ and the angle between $\alpha$ and $\beta$ is $\dfrac{\pi}{3}$, then the length of a diagonal of the parallelogram is
- Every group of order 7 is
- Let $U_{n} = 2 + 2^{3} + 2^{5} + \cdots + 2^{2n+1}$ and $V_{n} = 1 + 4 + 4^{2} + \cdots + 4^{n-1}$. Then $\displaystyle\lim_{n \to \infty} \dfrac{U_n}{V_n}$ is equal to
View More Questions
Top MET Circles Questions
- The difference of the focal distances of any point on the hyperbola is equal to its
- The locus of the point of intersection of two perpendicular tangents to a circle is called
- Consider the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the area of the triangle formed by the asymptotes and the tangent drawn to it at $(a,0)$ is
- The normal at the point (3, 4) on a circle cuts the circle at the point (-1, -2). Then the equation of the circle is
- The equation of the parabola whose vertex is (-1, -2), axis is vertical and which passes through the point (3, 6), is
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions