Q66 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Mathematics

The length of the chord intercepted by the circle \(x^2+y^2-6 x+8 y-5=0\) on the line \(2 x-y=5\) is equal to units

  • Correct answer
    A
    10
  • B
    12
  • C
    7
  • D
    8

Solution

Centre \(=(3,-4)\) \(\text {Radius }=\sqrt{9+16+5}=\sqrt{30}\) \(d=\) Perpendicular distance from \((3,-4)\) to the chord \(2 x-y-5=0\) \(\begin{aligned} d & =\frac{|2(3)-(-4)-5|}{\sqrt{4+1}} \\ d & =\frac{|6+4-5|}{\sqrt{5}} \\ d & =\sqrt{5} \\ \text { length of chord } & =2 \sqrt{r^2-d^2}=2 \sqrt{30-5} \\ & =2 \times 5=10 \text { units } \end{aligned}\) Hence, option (a) is correct.

Hence, the correct answer is option: 'A'.

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