AP EAMCET · Maths · Circle
The slope of the non-vertical tangent drawn from the point \((3,4)\) to the circle \(x^2+y^2=9\) is
- A \(\frac{2}{3}\)
- B \(\frac{3}{2}\)
- C \(\frac{7}{24}\)
- D \(\frac{24}{7}\)
Answer & Solution
Correct Answer
(C) \(\frac{7}{24}\)
Step-by-step Solution
Detailed explanation
\(y-4 = m(x-3)\) \(mx-y+(4-3m)=0\) \(\frac{|m(0)-(0)+(4-3m)|}{\sqrt{m^2+(-1)^2}} = 3\) \((4-3m)^2 = 9(m^2+1)\) \(16-24m+9m^2 = 9m^2+9\) \(-24m = 9-16\) \(-24m = -7\) \(m = \frac{7}{24}\)
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