Question:
If P and Q are the points of intersection of the circles $x^2 + y^2 + 3x + 7y + 2p - 5 = 0$ and $x^2 + y^2 + 2x + 2y - p^2 = 0$ , then there is a circle passing through $P, Q$ and $(1, 1)$ for
If P and Q are the points of intersection of the circles $x^2 + y^2 + 3x + 7y + 2p - 5 = 0$ and $x^2 + y^2 + 2x + 2y - p^2 = 0$ , then there is a circle passing through $P, Q$ and $(1, 1)$ for
Updated On: Jul 28, 2022
- all values of p
- all except one value of p
- all except two values of p
- exactly one value of p
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Given circles $S = x^2 + y^2 + 3x + 7y + 2p - 5 = 0$
$S' = x^2 + y^2 + 2x + 2y - p^2 = 0$
Equation of required circle is $S+\lambda S '=0$
As it passes through $\left(1, 1\right)$ the value of $\lambda=\frac{-\left(7+2p\right)}{\left(6-p^{2}\right)}M$
If $7 + 2p = 0$, it becomes the second circle
$\therefore$ it is true for all values of $p$
Was this answer helpful?
0
0
Top Questions on Conic sections
- Let \[ E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad a > b \quad \text{and} \quad H: \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1. \] Let the distance between the foci of \( E \) and the foci of \( H \) be \( 2\sqrt{3} \). If \( a - A = 2 \), and the ratio of the eccentricities of \( E \) and \( H \) is \( \frac{1}{3} \), then the sum of the lengths of their latus rectums is equal to:
- JEE Main - 2025
- Mathematics
- Conic sections
- Let \[ E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad a > b \quad \text{and} \quad H: \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1. \] Let the distance between the foci of \( E \) and the foci of \( H \) be \( 2\sqrt{3} \). If \( a - A = 2 \), and the ratio of the eccentricities of \( E \) and \( H \) is \( \frac{1}{3} \), then the sum of the lengths of their latus rectums is equal to:
- JEE Main - 2025
- Mathematics
- Conic sections
- The area bounded by \( y - 1 = |x| \) and \( y + 1 = |x| \) is: (a) \( \frac{1}{2} \)
- VITEEE - 2024
- Mathematics
- Conic sections
If a tangent to the hyperbola \( x^2 - \frac{y^2}{3} = 1 \) is also a tangent to the parabola \( y^2 = 8x \), then the equation of such tangent with the positive slope is:
- AP EAPCET - 2024
- Mathematics
- Conic sections
If a circle of radius 4 cm passes through the foci of the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and is concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola is:
- AP EAPCET - 2024
- Mathematics
- Conic sections
View More Questions
Questions Asked in AIEEE exam
- This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. It is not possible to make a sphere of capacity $1$ farad using a conducting material. It is possible for earth as its radius is $6.4 \times 10^6\,m$.
- AIEEE - 2012
- electrostatic potential and capacitance
- A steel wire can sustain $100\, kg$ weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of
- AIEEE - 2012
- mechanical properties of solids
- The limiting line in Balmer series will have a frequency of (Rydberg constant, $R_{\infty}=3.29\times10^{15}$ cycles/s)
- AIEEE - 2012
- Electromagnetic Spectrum
- Which of the plots shown in the figure represents speed (v) of the electron in a hydrogen atom as a function of the principal quantum number (n)?
- The ratio of number of oxygen atoms (O) in 16.0 g ozone $(O_3), \,28.0\, g$ carbon monoxide $(CO)$ and $16.0$ oxygen $(O_2)$ is (Atomic mass: $C = 12,0 = 16$ and Avogadro?? constant $N_A = 6.0 x 10^{23}\, mol^{-1}$)
- AIEEE - 2012
- Mole concept and Molar Masses
View More Questions