AP EAMCET · Maths · Circle
The length of the tangent drawn from the mid-point of the line joining the origin and the point \((4,-4)\), to the circle \(2 x^2+2 y^2-y=0\) is units
- A \(3 \sqrt{2}\)
- B \(\sqrt{2}\)
- C \(\sqrt{10}\)
- D 3
Answer & Solution
Correct Answer
(D) 3
Step-by-step Solution
Detailed explanation
The mid-point of line joining origin and the point \((4,-4)\) is \(P(2,-2)\), so the length of tangent drawn from point \(P(2,-2)\) to the given circle \(2 x^2+2 y^2-y=0\) or \(x^2+y^2-\frac{y}{2}=0\) is \[ \sqrt{(2)^2+(-2)^2-\frac{(-2)}{2}}=\sqrt{4+4+1}=3 \text { units. } \]
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