Question:
If the circles \( x^2+y^2-8x-6y+c=0 \) and \( x^2+y^2-2y+d=0 \) cut orthogonally, then \( c+d \) equals
If the circles \( x^2+y^2-8x-6y+c=0 \) and \( x^2+y^2-2y+d=0 \) cut orthogonally, then \( c+d \) equals
Show Hint
Use standard form \(x^2+y^2+2gx+2fy+c=0\).
Updated On: Apr 30, 2026
- \(6\)
- \(4\)
- \(2\)
- \(0\)
- \(1\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
Orthogonal circles condition:
\[
2(g_1g_2 + f_1f_2) = c_1 + c_2
\]
Step 1: Compare equations. First circle: \[ g_1=-4, f_1=-3 \] Second: \[ g_2=0, f_2=-1 \]
Step 2: Apply condition. \[ 2((-4)(0)+(-3)(-1)) = c+d \] \[ 2(3) = c+d \] \[ c+d=6 \]
Step 1: Compare equations. First circle: \[ g_1=-4, f_1=-3 \] Second: \[ g_2=0, f_2=-1 \]
Step 2: Apply condition. \[ 2((-4)(0)+(-3)(-1)) = c+d \] \[ 2(3) = c+d \] \[ c+d=6 \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM circle Questions
- If one end of a diameter of the circle \( x^2 + y^2 - 4x - 6y + 11 = 0 \) is \( (3, 4) \), then the coordinate of the other end of the diameter is:
- Find the area of the smaller segment cut-off from the circle \( x^2 + y^2 = 25 \) by \( x = 3 \):
- If the point \( (2, k) \) lies on the circle \( (x - 2)^2 + (y + 1)^2 = 4 \), then the value of \( k \) is:
- The radius of the circle \( x^2 + y^2 - 2x - 4y - 4 = 0 \) is:
- If the parametric form of the circle is \( x = 3\cos\theta + 3 \) and \( y = 3\sin\theta \), then the Cartesian form of the equation of the circle is:
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions