MHT CET · Maths · Circle
Let the equation of circle is \(x^{2}+y^{2}-6 x-4 y+9=0\). Then the line \(4 x+3 y-8=0\) is a
- A tangent of the circle
- B normal of the circle
- C chord of the circle
- D None of the above
Answer & Solution
Correct Answer
(A) tangent of the circle
Step-by-step Solution
Detailed explanation
Given circle is \(x^{2}+y^{2}-6 x-4 y+9=0\)
\(C=(3,2), r=2\)
If line \(4 x+3 y-8=0\) is a tangent to the circle, then
\(
\left|\frac{4(3)+3(2)-8}{\sqrt{16+9}}\right|=2
\)
\(\Rightarrow \left|\frac{10}{5}\right|=2 \Rightarrow 2=2\)
Hence, it is a tangent of the circle.
\(C=(3,2), r=2\)
If line \(4 x+3 y-8=0\) is a tangent to the circle, then
\(
\left|\frac{4(3)+3(2)-8}{\sqrt{16+9}}\right|=2
\)
\(\Rightarrow \left|\frac{10}{5}\right|=2 \Rightarrow 2=2\)
Hence, it is a tangent of the circle.
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