AP EAMCET · Maths · Parabola
The lengths of the two focal chords of the parabola \(y^2=16 x\) is 25 units each. If these two chords cut the parabola at A, B, C and D, then the area (in sq. units) of the quadrilateral formed by \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and D is
- A \(\frac{625}{2}\)
- B \(180\)
- C \(150\)
- D \(300\)
Answer & Solution
Correct Answer
(D) \(300\)
Step-by-step Solution
Detailed explanation
\(y^2=16x \implies 4a=16 \implies a=4\) Length of focal chord \(L = a(t+1/t)^2\) \(25 = 4(t+1/t)^2 \implies (t+1/t)^2 = 25/4 \implies t+1/t = 5/2\) \(2t^2-5t+2=0 \implies (2t-1)(t-2)=0 \implies t=2 \text{ or } t=1/2\) For the first chord (let \(t=2\)): Endpoints \((at^2, 2at)\)…
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