TS EAMCET · Maths · Straight Lines
If \(M\) is the foot of the perpendicular drawn from the origin \(O\) on to the variable line \(L\), passing through a fixed point \((a, b)\), then the locus of the mid-point of \(O M\) is
- A \(x^2+y^2=a^2+b^2\)
- B \(2 x^2+2 y^2-a x-b y=0\)
- C \(a x+b y=0\)
- D \(2 x^2+2 y^2-a y-b x=0\)
Answer & Solution
Correct Answer
(B) \(2 x^2+2 y^2-a x-b y=0\)
Step-by-step Solution
Detailed explanation
We have, \(R(h, k)\) is mid-point of \(O M\). \(\therefore \quad\left(\frac{0+\alpha}{2}, \frac{0+\beta}{2}\right)=(h, k) \Rightarrow \alpha=2 h, \beta=2 k\) \(\Rightarrow\) Coordinates of \(M\) are \((2 h, 2 k)\). Now, slope of \(O M=\frac{2 k-0}{2 h-0}=\frac{k}{h}\) and slope…
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