If the focus of a parabola divides a focal chord of the parabola into segments of lengths 5,3 units, then…

If the focus of a parabola divides a focal chord of the parabola into segments of lengths 5,3 units, then the length of the latusrectum of that parabola is
  1. $\frac{15}{4}$
  2. 20
  3. $\frac{25}{2}$
  4. $\frac{15}{2}$

Solution

Since, semi latusrectum is the harmonic mean of segments. So, semi laturectum length $=\frac{2 \times 5 \times 3}{5+3}=\frac{30}{8}=\frac{15}{4}$ $\therefore \quad$ Length of latusrectum $=2 \times \frac{15}{4}=\frac{15}{2}$

Asked in: AP EAMCET 2019 (21 Apr Shift 1)

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