If the circles x^2 + y^2 + 5Kx + 2y + K = 0 a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The equation of the first circle is $S_1: x^2 + y^2 + 5Kx + 2y + K = 0$.The equation of the second circle is $S_2: x^2 + y^2 + Kx + \frac{3}{2}y -

Vedclass · Accepted Answer

no value of $K$

Vedclass · Answer

(B) The equation of the first circle is $S_1: x^2 + y^2 + 5Kx + 2y + K = 0$.The equation of the second circle is $S_2: x^2 + y^2 + Kx + \frac{3}{2}y - \frac{1}{2} = 0$.The common chord of two circles $S_1 = 0$ and $S_2 = 0$ is given by $S_1 - S_2 = 0$.$(x^2 + y^2 + 5Kx + 2y + K) - (x^2 + y^2 + Kx + \frac{3}{2}y - \frac{1}{2}) = 0$$4Kx + \frac{1}{2}y + K + \frac{1}{2} = 0$.This line is identical to the given line $4x + 5y - K = 0$.Comparing the coefficients,we have $\frac{4K}{4} = \frac{1/2}{5} = \frac{K + 1/2}{-K}$.From $\frac{4K}{4} = \frac{1}{10}$,we get $K = \frac{1}{10}$.Checking the second equality: $\frac{1}{10} = \frac{1/10 + 1/2}{-1/10} = \frac{6/10}{-1/10} = -6$.Since $K = \frac{1}{10} 
eq -6$,there is no value of $K$ for which the lines are identical.

If the circles $x^2 + y^2 + 5Kx + 2y + K = 0$ and $2(x^2 + y^2) + 2Kx + 3y - 1 = 0$,$(K \in R)$,intersect at the points $P$ and $Q$,then the line $4x + 5y - K = 0$ passes through $P$ and $Q$ for

Similar Questions

The point of intersection of the direct common tangents drawn to the circles $(x+11)^2+(y-2)^2=225$ and $(x-11)^2+(y+2)^2=25$ is

If the circles $x^2 + y^2 + 2ax + cy + a = 0$ and $x^2 + y^2 - 3ax + dy - 1 = 0$ intersect at two distinct points $P$ and $Q$,then for what value of $a$ does the line $5x + 6y - a = 0$ pass through points $P$ and $Q$?

Tangents $AB$ and $AC$ are drawn from the point $A(0, 1)$ to the circle $x^2 + y^2 - 2x + 4y + 1 = 0$. The equation of the circle passing through $A, B,$ and $C$ is

The circle $S \equiv x^2+y^2-2x-4y+1=0$ cuts the $y$-axis at $A, B$ $(OA > OB)$. If the radical axis of $S=0$ and $S^{\prime} \equiv x^2+y^2-4x-2y+4=0$ cuts the $y$-axis at $C$,then the ratio in which $C$ divides $AB$ is:

If the line $x - 2y = k$ cuts off a chord of length $2$ from the circle ${x^2} + {y^2} = 3$,then $k =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module