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TS EAMCET · Maths · Circle

If a circle \(C_1: x^2+y^2=16\) intersects another circle \(C_2\) with radius 5 such that the common chord is of maximum length and has a slope equal to \(\frac{3}{4}\) then the centre of the circle \(C_2\) is

  1. A \(\left(-\frac{9}{5}, \frac{12}{5}\right)\)
  2. B \(\left(\frac{9}{5}, \frac{12}{5}\right)\)
  3. C \(\left(-\frac{5}{9}, \frac{6}{5}\right)\)
  4. D \(\left(\frac{7}{5},-\frac{12}{5}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\left(-\frac{9}{5}, \frac{12}{5}\right)\)

Step-by-step Solution

Detailed explanation

Given circle, \(C_1: x^2+y^2=16\) radius \(=4\) units, centre \((0,0)\) The maximum length of chord = the diameter of circle \(c_1=8\) units. The equation of chord passing through \((0,0)\) and slope \(\frac{3}{4}\) is \( y=\frac{3}{4} x \Rightarrow 3 x-4 y=0 \) The centre of…