AP EAMCET · Maths · Circle
If the circles \(x^2+y^2+2 h x+2 k y=0\) and \(x^2+y^2+2 h^{\prime} x+2 k^{\prime} y=0\) touch each other, then \(\frac{h^{\prime} k}{h k^{\prime}}=\)
- A \(0\)
- B \(1\)
- C \(2\)
- D \(-1\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
Tangent to \(x^2+y^2+2 h x+2 k y=0\) at \((0,0)\) is \(hx+ky=0\). Tangent to \(x^2+y^2+2 h^{\prime} x+2 k^{\prime} y=0\) at \((0,0)\) is \(h^{\prime}x+k^{\prime}y=0\). For the circles to touch at the origin, the tangents must be identical:…
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