TS EAMCET · Maths · Parabola
If the points of intersection of the parabolas \(y^2=5 x\) and \(x^2=5 y\) lie on the line L, then the area of the triangle formed by the directrix of one parabola, latus rectum of another parabola and the line \(\mathrm{L}\) is
- A \(\frac{15}{32}\)
- B \(\frac{12}{25}\)
- C \(\frac{25}{8}\)
- D \(\frac{25}{32}\)
Answer & Solution
Correct Answer
(C) \(\frac{25}{8}\)
Step-by-step Solution
Detailed explanation
\(y^2=5 x\)...(i) \(x^2=5 y\)...(ii) Solving (i) \& (ii) \( \begin{aligned} & \left(\frac{x^2}{5}\right)^2=5 x \\ & x^4=x .5^3 \\ & \therefore x=0,5 \Rightarrow y=0,5 \end{aligned} \) Point of intersection \((0,0),(5,5)\) \(\therefore {L} \equiv y=x\)...(1) Equation of directix…
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