CircleHardBloom L3
Question
The locus of the center of the circles such that the point $(2,3)$ is the mid point of the chord $5x + 2y = 16$ is:
Options
A.$2x - 5y + 11 = 0$
B.$2x + 5y - 11 = 0$
C.$2x + 5y + 11 = 0$
D.none of these
Solution
Sol. [Key Concept: Locus of the centre with $(2,3)$ the midpoint of a chord: use the midpoint-chord relation $T = S_{1}$.]
$$\begin{matrix} & \frac{k - 3}{h - 2} = \frac{2}{5} \\ & 5k = 2h + 11 \\ & 2x - 5y + 11 = 0 \end{matrix}$$
Create a free account to view solution
View Solution FreeMore Circle Questions
If (4, 3) and (−12, −1) are end points of a diameter of a circle, then the equation of the circle is-...If a circle with centre (0, 0) touches the line 5x + 12y = 1 then its equation will be-...A variable circle is drawn to touch the x-axis at the origin. The locus of the pole of the straight line lx + my + n = 0...The parametric coordinates of any point on the circle x2 + y2 - 4x - 4y = 0 are -...The x coordinates of two points A and B are roots of equation x2 + 2x − a2 = 0 and y coordinate are roots of equat...