The radius of the circle
\( x^{2} + y^{2} - 4x + 6y - 12 = 0 \)
is:
Show Hint
- 5
- 25
- 12
- 7
The Correct Option is A
Solution and Explanation
For the circle $x^2 + y^2 + 2gx + 2fy + c = 0$, radius $r = \sqrt{g^2 + f^2 - c}$.
Step 2: Analysis
$2g = -4 \Rightarrow g = -2$; $2f = 6 \Rightarrow f = 3$; $c = -12$.
$r = \sqrt{(-2)^2 + (3)^2 - (-12)} = \sqrt{4 + 9 + 12}$.
Step 3: Conclusion
$r = \sqrt{25} = 5$.
Final Answer: (A)
Top MET Mathematics Questions
- If \(f(x) = \begin{cases} x, & 0 \le x \le 1 \\ 2x - 1, & 1<x \end{cases}\), then
- MET - 2019
- Mathematics
- Continuity
- The remainder obtained when \(5^{124}\) is divided by 124 is
- MET - 2019
- Mathematics
- Number Theory
- The adjoining graph
- MET - 2019
- Mathematics
- Graph Theory
- If \(I_n = \int \sin^n x dx\), then \(nI_n - (n - 1)I_{n-2}\) equals
- MET - 2019
- Mathematics
- Integral Calculus
- If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is
Top MET circle Questions
- The point \( (3, -4) \) lies on both the circles \( x^{2} + y^{2} - 2x + 8y + 13 = 0 \) and \( x^{2} + y^{2} - 4x + 6y + 11 = 0 \). Then, the angle between the circles is
- The equation of the circle which passes through the origin and cuts orthogonally each of the circles \( x^{2} + y^{2} - 6x + 8 = 0 \) and \( x^{2} + y^{2} - 2x - 2y = 7 \) is
- If the circle \( x^{2} + y^{2} = a^{2} \) intersects the hyperbola \( xy = c^{2} \) in four points \( (x_i, y_i) \), for \( i = 1, 2, 3, 4 \), then \( y_{1} + y_{2} + y_{3} + y_{4} \) equals
- The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x and y-axes respectively are
- The locus of centre of a circle which passes through the origin and cuts off a length of 4 unit from the line $x=3$ is
Top MET Questions
- 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 :
- MET - 2020
- Photoelectric Effect
- If \(f(x) = \begin{cases} x, & 0 \le x \le 1 \\ 2x - 1, & 1<x \end{cases}\), then
- MET - 2019
- Continuity
Helicopters are very different from airplanes. They can do three things that airplanes cannot do. First, when airplanes move upward, they must also move forward, but helicopters can move straight up without moving ahead. Second, helicopters can fly backward, which airplanes cannot do. Third, helicopters can use their rotors to hover in the air, which is impossible for airplanes. Helicopters can perform actions that airplanes cannot, they are used for different tasks. Since, helicopters can take off without moving forward, they do not need a runway for take off. They are used in congested areas where there is no room for airplanes or in isolated areas, which do not have airports. Because they can hover, they are used on firefighting missions to drop water on fires. They are used in logging operations to lift trees out of forests. Helicopters are used as air ambulances to airlift patients out of situations, which are difficult to reach by conventional ambulances. The police used helicopters to follow suspects on the ground or to search for cars on the ground. Of course, helicopters have military uses because of their design and capabilities.
- MET - 2019
- Reading Comprehension
- Find the missing character.
- MET - 2019
- Number Patterns
- 6, 9, 12, 15, 18, ?
- MET - 2019
- Number Patterns