TS EAMCET · Maths · Parabola
If \(P\) is \((3,1)\) and \(Q\) is a point on the curve \(y^2=8 x\), then the locus of the mid-point of the line segment \(P Q\) is
- A \(4 y^2-12 x-6 y+21=0\)
- B \(4 y^2-16 x-4 y+25=0\)
- C \(4 y^2+8 x-3 y-18=0\)
- D \(4 y^2-12 x+8 y-15=0\)
Answer & Solution
Correct Answer
(B) \(4 y^2-16 x-4 y+25=0\)
Step-by-step Solution
Detailed explanation
\( \text {} P(3,1) \text { and } Q \text { is a point of parabola } y^2=8 x \) \( \text { Let } R_{(h, k)} \text { is the mid-point of } P Q \text {. } \) So, coordinate of \(Q(2 h-3,2 k-1)\) point \(Q\) lie on parabola, so \((2 k-1)^2=8(2 h-3)\)…
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