Coordinate Geometry
Circles
MMTS_Full_Test_04
Grade 12
Question:
If the circle $C_1:x^2+y^2=16$ intersects another circle $C_2$ of radius 5, in such a manner that the common chord is of maximum length and has a slope equal to $3/4$, then one of the co-ordinates of the centre of $C_2$ are
$\left(\dfrac{9}{5},\dfrac{12}{5}\right)$
$\left(\dfrac{9}{5},-\dfrac{12}{5}\right)$
$\left(\dfrac{12}{5},\dfrac{9}{5}\right)$
$\left(\dfrac{12}{5},-\dfrac{9}{5}\right)$
Step-by-Step Solution
Key Concept: Max chord length means chord is diameter of Cā; centre of Cā lies on perpendicular to chord
Perpendicular to slope 3/4 has slope $-4/3$. Centre of Cā on this line at distance 5 from origin: $(9/5,-12/5)$.
Correct Answer: 2