TS EAMCET · Maths · Circle
If \(m\) is the slope and \(P(8, \beta)\) is the midpoint of a chord of contact of the circle \(x^2+y^2=125\), then the number of values of \(\beta\) such that \(\beta\) and \(m\) are integers is
- A 2
- B 4
- C 6
- D 8
Answer & Solution
Correct Answer
(C) 6
Step-by-step Solution
Detailed explanation
Given circle is \(x^2+y^2=125\) and mid point of chord is \(P(8, \beta)\) Eq. of chord with mid point \(P(8, \beta)\) is \(T=S_1\) \(\Rightarrow 8 x+\beta y-64-\beta^2=0\) Slope of chord is, \(m=\frac{-8}{\beta}\) As \(m\) is an integer So \(\beta= \pm 1, \pm 2, \pm 4, \pm 8\)…
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