AP EAMCET · Maths · Parabola
\(\mathrm{A}=(-2,0)\) and \(\mathrm{P}\) is a point on the parabola \(y^2=8 x\). If \(\mathrm{Q}\) bisects \(\overline{\mathrm{AP}}\) and the locus of \(\mathrm{Q}\) is a parabola, then its focus is
- A \((0,0)\)
- B \((1,1)\)
- C \((5,0)\)
- D \((4,0)\)
Answer & Solution
Correct Answer
(A) \((0,0)\)
Step-by-step Solution
Detailed explanation
Let \(P=(x_p, y_p)\) be a point on the parabola \(y^2=8x\), so \(y_p^2 = 8x_p\). Let \(Q=(x,y)\) be the midpoint of \(A(-2,0)\) and \(P(x_p, y_p)\). \(x = \frac{x_p - 2}{2} \Rightarrow x_p = 2x + 2\) \(y = \frac{y_p + 0}{2} \Rightarrow y_p = 2y\) Substitute \(x_p, y_p\) into the…
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