TS EAMCET · Maths · Pair of Lines
The condition that the lines joining the origin to the points of intersection of the two curves \(x^2+y^2+g x+c=0, x^2+y^2+2 f y-c=0\) are at right angles, is
- A \(g^2-f^2=4 c\)
- B \(g^2-f^2=2 c\)
- C \(f^2-4 g^2=8 c\)
- D \(g^2-4 f^2=8 c\)
Answer & Solution
Correct Answer
(D) \(g^2-4 f^2=8 c\)
Step-by-step Solution
Detailed explanation
Equation of curves are, \(x^2+y^2+g x+c=0 \text { and } x^2+y^2+2 f y-c=0\) Subtract Eq. (i) from Eq. (ii), we get \(2 f y-g x=2 c \Rightarrow \frac{2 f y-g x}{2 c}=1\) Homogeneousing the Eq. (i), we get…
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