TS EAMCET · Maths · Circle
If \(h k p q \neq 0\) and the circles \(x^2+y^2+2 h x+2 k y=0\) and \(x^2+y^2+2 p x+2 q y=0\) touch each other at the origin, then \(h q-p k-\frac{h q}{p k}\) is equal to
- A −1
- B 0
- C 1
- D 2
Answer & Solution
Correct Answer
(A) −1
Step-by-step Solution
Detailed explanation
As we know that two circles \[ \begin{aligned} & x^2+y^2+2 g x+2 f y=0 \text { and } \\ & x^2+y^2+2 g^{\prime} x+2 f^{\prime} y=0 \text { touch each other } \\ & \text { if } g f^{\prime}=g^{\prime} f \end{aligned} \] So, circles given in question, touch each other if…
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